Class XI Chapter **11** – Conic Section Maths ______________________________________________________________________________ Since the centre (h, k) of the circle lies on line 4x + y = 16, 4h + k = 16 … (3) From equations (1) and (2), we obtain (4 â€“ h) 2 + (1 â€“ k) 2 = (6 â€“ h) 2 + (5 â€“ k)2 ⇒ 16 â€“ 8h + h 2 + 1 â€“ 2k + k 2 = 36 â€“ 12h + h 2 + 25 â€“ 10k + k 2 ⇒ 16 â€“ 8h + 1 â€“ 2k = 36 â€“ 12h + 25 â€“ 10k ⇒ 4h + 8k = 44 ⇒ h + 2k = **11** … (4) On solving equations (3) and (4), we obtain h = 3 and k = 4. On substituting the values of h and k in equation (1), we obtain (4 â€“ 3) 2 + (1 â€“ 4) 2 = r 2 ⇒ (1) 2 + (â€“ 3) 2 = r2 ⇒ 1 + 9 = r 2 ⇒ r 2 = 10 ⇒ r = 10 Thus, the equation of the required circle is (x â€“ 3) 2 + (y â€“ 4) 2 = 2 10 X 2 â€“ 6x + 9 + y 2 â€“ 8y + 16 = 10 X 2 + y 2 â€“ 6x â€“ 8y + 15 = 0 Question **11**: Find the equation of the circle passing through the points (2, 3) and (-1, 1) and whose centre is on the line x- 3y - **11** = 0. Solution **11**: Let the equation of the required circle be (x â€“ h) 2 + (y â€“ k) 2 = r 2 . Since the circle passes through points (2, 3) and (â€“1, 1), (2 â€“ h) 2 + (3 â€“ k) 2 = r 2 … (1) (â€“1 â€“ h) 2 + (1 â€“ k) 2 = r 2 … (2) Since the centre (h, k) of the circle lies on line x â€“ 3y â€“ **11** = 0, h â€“ 3k = **11** … (3) From equations (1) and (2), we obtain (2 â€“ h) 2 + (3 â€“ k) 2 = (â€“1 â€“ h) 2 + (1 â€“ k) 2 ⇒ 4 â€“ 4h + h 2 + 9 â€“ 6k + k 2 = 1 + 2h + h 2 + 1 â€“ 2k + k 2 ⇒ 4 â€“ 4h + 9 â€“ 6k = 1 + 2h + 1 â€“ 2k ⇒ 6h + 4k = **11** … (4) Printed from Vedantu.com. Register now to book a Free LIVE Online trial session with a Top tutor.

Class XI Chapter **11** – Conic Section Maths ______________________________________________________________________________ On solving equations (3) and (4), we obtain h = 7 2 and k = 5 2 On substituting the values of h and k in equation (1), we obtain 2 2 7 5 2 3 r 2 2 2 2 47 65 r 2 2 2 2 3 **11** 2 2 r 2 9 121 2 r 4 4 130 2 r 4 Thus, the equation of the required circle is 2 2 7 5 130 x y 2 2 4 2 2 2x7 2y5 130 2 2 4 2 2 4x 28x 49 4y 20y 25 130 2 2 4x 4y 28x 20y 56 0 2 2 4 x y 7x 5y 14 0 2 2 x y x y 7 5 14 0 2 2 Question 12: Find the equation of the circle with radius 5 whose centre lies on x-axis and passes through the point (2, 3). Solution 12: Let the equation of the required circle be (x â€“ h) 2 + (y â€“ k) 2 = r 2 . Since the radius of the circle is 5 and its centre lies on the x-axis, k = 0 and r = 5. Now, the equation of the circle becomes (x â€“ h) 2 + y 2 = 25. It is given that the circle passes through point (2, 3). Printed from Vedantu.com. Register now to book a Free LIVE Online trial session with a Top tutor.

- Page 1 and 2:
Class XI Chapter 1 - Sets Maths ___

- Page 3 and 4:
Class XI Chapter 1 - Sets Maths ___

- Page 5 and 6:
Class XI Chapter 1 - Sets Maths ___

- Page 7 and 8:
Class XI Chapter 1 - Sets Maths ___

- Page 9 and 10:
Class XI Chapter 1 - Sets Maths ___

- Page 11 and 12:
Class XI Chapter 1 - Sets Maths ___

- Page 13 and 14:
Class XI Chapter 1 - Sets Maths ___

- Page 15 and 16:
Class XI Chapter 1 - Sets Maths ___

- Page 17 and 18:
Class XI Chapter 1 - Sets Maths ___

- Page 19 and 20:
Class XI Chapter 1 - Sets Maths ___

- Page 21 and 22:
Class XI Chapter 1 - Sets Maths ___

- Page 23 and 24:
Class XI Chapter 1 - Sets Maths ___

- Page 25 and 26:
Class XI Chapter 1 - Sets Maths ___

- Page 27 and 28:
Class XI Chapter 1 - Sets Maths ___

- Page 29 and 30:
Class XI Chapter 1 - Sets Maths ___

- Page 31 and 32:
Class XI Chapter 1 - Sets Maths ___

- Page 33 and 34:
Class XI Chapter 1 - Sets Maths ___

- Page 35 and 36:
Class XI Chapter 1 - Sets Maths ___

- Page 37 and 38:
Class XI Chapter 1 - Sets Maths ___

- Page 39 and 40:
Class XI Chapter 1 - Sets Maths ___

- Page 41 and 42:
Class XI Chapter 1 - Sets Maths ___

- Page 43 and 44:
Class XI Chapter 2 - Relations and

- Page 45 and 46:
Class XI Chapter 2 - Relations and

- Page 47 and 48:
Class XI Chapter 2 - Relations and

- Page 49 and 50:
Class XI Chapter 2 - Relations and

- Page 51 and 52:
Class XI Chapter 2 - Relations and

- Page 53 and 54:
Class XI Chapter 2 - Relations and

- Page 55 and 56:
Class XI Chapter 2 - Relations and

- Page 57 and 58:
Class XI Chapter 2 - Relations and

- Page 59 and 60:
Class XI Chapter 2 - Relations and

- Page 61 and 62:
Class XI Chapter 3 - Trigonometric

- Page 63 and 64:
Class XI Chapter 3 - Trigonometric

- Page 65 and 66:
Class XI Chapter 3 - Trigonometric

- Page 67 and 68:
Class XI Chapter 3 - Trigonometric

- Page 69 and 70:
Class XI Chapter 3 - Trigonometric

- Page 71 and 72:
Class XI Chapter 3 - Trigonometric

- Page 73 and 74:
Class XI Chapter 3 - Trigonometric

- Page 75 and 76:
Class XI Chapter 3 - Trigonometric

- Page 77 and 78:
Class XI Chapter 3 - Trigonometric

- Page 79 and 80:
Class XI Chapter 3 - Trigonometric

- Page 81 and 82:
Class XI Chapter 3 - Trigonometric

- Page 83 and 84:
Class XI Chapter 3 - Trigonometric

- Page 85 and 86:
Class XI Chapter 3 - Trigonometric

- Page 87 and 88:
Class XI Chapter 3 - Trigonometric

- Page 89 and 90:
Class XI Chapter 3 - Trigonometric

- Page 91 and 92:
Class XI Chapter 3 - Trigonometric

- Page 93 and 94:
Class XI Chapter 3 - Trigonometric

- Page 95 and 96:
Class XI Chapter 3 - Trigonometric

- Page 97 and 98:
Class XI Chapter 3 - Trigonometric

- Page 99 and 100:
Class XI Chapter 4 - Principle of M

- Page 101 and 102:
Class XI Chapter 4 - Principle of M

- Page 103 and 104:
Class XI Chapter 4 - Principle of M

- Page 105 and 106:
Class XI Chapter 4 - Principle of M

- Page 107 and 108:
Class XI Chapter 4 - Principle of M

- Page 109 and 110:
Class XI Chapter 4 - Principle of M

- Page 111 and 112:
Class XI Chapter 4 - Principle of M

- Page 113 and 114:
Class XI Chapter 4 - Principle of M

- Page 115 and 116:
Class XI Chapter 4 - Principle of M

- Page 117 and 118:
Class XI Chapter 4 - Principle of M

- Page 119 and 120:
Class XI Chapter 4 - Principle of M

- Page 121 and 122:
Class XI Chapter 4 - Principle of M

- Page 123 and 124:
Class XI Chapter 4 - Principle of M

- Page 125 and 126:
Class XI Chapter 5 - Complex Number

- Page 127 and 128:
Class XI Chapter 5 - Complex Number

- Page 129 and 130:
Class XI Chapter 5 - Complex Number

- Page 131 and 132:
Class XI Chapter 5 - Complex Number

- Page 133 and 134:
Class XI Chapter 5 - Complex Number

- Page 135 and 136:
Class XI Chapter 5 - Complex Number

- Page 137 and 138:
Class XI Chapter 5 - Complex Number

- Page 139 and 140:
Class XI Chapter 5 - Complex Number

- Page 141 and 142:
Class XI Chapter 5 - Complex Number

- Page 143 and 144:
Class XI Chapter 5 - Complex Number

- Page 145 and 146:
Class XI Chapter 5 - Complex Number

- Page 147 and 148:
Class XI Chapter 5 - Complex Number

- Page 149 and 150:
Class XI Chapter 5 - Complex Number

- Page 151 and 152:
Class XI Chapter 5 - Complex Number

- Page 153 and 154:
Class XI Chapter 5 - Complex Number

- Page 155 and 156:
Class XI Chapter 6 - Linear Inequal

- Page 157 and 158:
Class XI Chapter 6 - Linear Inequal

- Page 159 and 160:
Class XI Chapter 6 - Linear Inequal

- Page 161 and 162:
Class XI Chapter 6 - Linear Inequal

- Page 163 and 164:
Class XI Chapter 6 - Linear Inequal

- Page 165 and 166:
Class XI Chapter 6 - Linear Inequal

- Page 167 and 168:
Class XI Chapter 6 - Linear Inequal

- Page 169 and 170:
Class XI Chapter 6 - Linear Inequal

- Page 171 and 172:
Class XI Chapter 6 - Linear Inequal

- Page 173 and 174:
Class XI Chapter 6 - Linear Inequal

- Page 175 and 176:
Class XI Chapter 6 - Linear Inequal

- Page 177 and 178:
Class XI Chapter 6 - Linear Inequal

- Page 179 and 180:
Class XI Chapter 6 - Linear Inequal

- Page 181 and 182:
Class XI Chapter 6 - Linear Inequal

- Page 183 and 184:
Class XI Chapter 6 - Linear Inequal

- Page 185 and 186:
Class XI Chapter 6 - Linear Inequal

- Page 187 and 188:
Class XI Chapter 6 - Linear Inequal

- Page 189 and 190:
Class XI Chapter 6 - Linear Inequal

- Page 191 and 192:
Class XI Chapter 6 - Linear Inequal

- Page 193 and 194:
Class XI Chapter 6 - Linear Inequal

- Page 195 and 196:
Class XI Chapter 6 - Linear Inequal

- Page 197 and 198:
Class XI Chapter 7 - Permutation an

- Page 199 and 200:
Class XI Chapter 7 - Permutation an

- Page 201 and 202:
Class XI Chapter 7 - Permutation an

- Page 203 and 204:
Class XI Chapter 7 - Permutation an

- Page 205 and 206:
Class XI Chapter 7 - Permutation an

- Page 207 and 208:
Class XI Chapter 7 - Permutation an

- Page 209 and 210:
Class XI Chapter 7 - Permutation an

- Page 211 and 212:
Class XI Chapter 7 - Permutation an

- Page 213 and 214:
Class XI Chapter 7 - Permutation an

- Page 215 and 216:
Class XI Chapter 7 - Permutation an

- Page 217 and 218:
Class XI Chapter 7 - Permutation an

- Page 219 and 220:
Class XI Chapter 8 - Binomial Theor

- Page 221 and 222:
Class XI Chapter 8 - Binomial Theor

- Page 223 and 224:
Class XI Chapter 8 - Binomial Theor

- Page 225 and 226:
Class XI Chapter 8 - Binomial Theor

- Page 227 and 228:
Class XI Chapter 8 - Binomial Theor

- Page 229 and 230:
Class XI Chapter 8 - Binomial Theor

- Page 231 and 232:
Class XI Chapter 8 - Binomial Theor

- Page 233 and 234:
Class XI Chapter 8 - Binomial Theor

- Page 235 and 236:
Class XI Chapter 8 - Binomial Theor

- Page 237 and 238:
Class XI Chapter 8 - Binomial Theor

- Page 239 and 240:
Class XI Chapter 8 - Binomial Theor

- Page 241 and 242:
Class XI Chapter 9 - Sequences and

- Page 243 and 244:
Class XI Chapter 9 - Sequences and

- Page 245 and 246:
Class XI Chapter 9 - Sequences and

- Page 247 and 248:
Class XI Chapter 9 - Sequences and

- Page 249 and 250:
Class XI Chapter 9 - Sequences and

- Page 251 and 252:
Class XI Chapter 9 - Sequences and

- Page 253 and 254:
Class XI Chapter 9 - Sequences and

- Page 255 and 256:
Class XI Chapter 9 - Sequences and

- Page 257 and 258:
Class XI Chapter 9 - Sequences and

- Page 259 and 260:
Class XI Chapter 9 - Sequences and

- Page 261 and 262:
Class XI Chapter 9 - Sequences and

- Page 263 and 264:
Class XI Chapter 9 - Sequences and

- Page 265 and 266:
Class XI Chapter 9 - Sequences and

- Page 267 and 268:
Class XI Chapter 9 - Sequences and

- Page 269 and 270:
Class XI Chapter 9 - Sequences and

- Page 271 and 272:
Class XI Chapter 9 - Sequences and

- Page 273 and 274:
Class XI Chapter 9 - Sequences and

- Page 275 and 276:
Class XI Chapter 9 - Sequences and

- Page 277 and 278:
Class XI Chapter 9 - Sequences and

- Page 279 and 280:
Class XI Chapter 9 - Sequences and

- Page 281 and 282:
Class XI Chapter 9 - Sequences and

- Page 283 and 284:
Class XI Chapter 9 - Sequences and

- Page 285 and 286:
Class XI Chapter 9 - Sequences and

- Page 287 and 288:
Class XI Chapter 9 - Sequences and

- Page 289 and 290:
Class XI Chapter 9 - Sequences and

- Page 291 and 292:
Class XI Chapter 9 - Sequences and

- Page 293 and 294:
Class XI Chapter 9 - Sequences and

- Page 295 and 296:
Class XI Chapter 9 - Sequences and

- Page 297 and 298:
Class XI Chapter 9 - Sequences and

- Page 299 and 300:
Class XI Chapter 9 - Sequences and

- Page 301 and 302:
Class XI Chapter 9 - Sequences and

- Page 303 and 304:
Class XI Chapter 9 - Sequences and

- Page 305 and 306:
Class XI Chapter 9 - Sequences and

- Page 307 and 308:
Class XI Chapter 9 - Sequences and

- Page 309 and 310:
Class XI Chapter 9 - Sequences and

- Page 311 and 312:
Class XI Chapter 9 - Sequences and

- Page 313 and 314:
Class XI Chapter 10 - Straight Line

- Page 315 and 316:
Class XI Chapter 10 - Straight Line

- Page 317 and 318:
Class XI Chapter 10 - Straight Line

- Page 319 and 320:
Class XI Chapter 10 - Straight Line

- Page 321 and 322:
Class XI Chapter 10 - Straight Line

- Page 323 and 324:
Class XI Chapter 10 - Straight Line

- Page 325 and 326: Class XI Chapter 10 - Straight Line
- Page 327 and 328: Class XI Chapter 10 - Straight Line
- Page 329 and 330: Class XI Chapter 10 - Straight Line
- Page 331 and 332: Class XI Chapter 10 - Straight Line
- Page 333 and 334: Class XI Chapter 10 - Straight Line
- Page 335 and 336: Class XI Chapter 10 - Straight Line
- Page 337 and 338: Class XI Chapter 10 - Straight Line
- Page 339 and 340: Class XI Chapter 10 - Straight Line
- Page 341 and 342: Class XI Chapter 10 - Straight Line
- Page 343 and 344: Class XI Chapter 10 - Straight Line
- Page 345 and 346: Class XI Chapter 10 - Straight Line
- Page 347 and 348: Class XI Chapter 10 - Straight Line
- Page 349 and 350: Class XI Chapter 10 - Straight Line
- Page 351 and 352: Class XI Chapter 10 - Straight Line
- Page 353 and 354: Class XI Chapter 10 - Straight Line
- Page 355 and 356: Class XI Chapter 10 - Straight Line
- Page 357 and 358: Class XI Chapter 10 - Straight Line
- Page 359 and 360: Class XI Chapter 10 - Straight Line
- Page 361 and 362: Class XI Chapter 10 - Straight Line
- Page 363 and 364: Class XI Chapter 10 - Straight Line
- Page 365 and 366: Class XI Chapter 10 - Straight Line
- Page 367 and 368: Class XI Chapter 10 - Straight Line
- Page 369 and 370: Class XI Chapter 10 - Straight Line
- Page 371 and 372: Class XI Chapter 10 - Straight Line
- Page 373 and 374: Class XI Chapter 11 - Conic Section
- Page 375: Class XI Chapter 11 - Conic Section
- Page 379 and 380: Class XI Chapter 11 - Conic Section
- Page 381 and 382: Class XI Chapter 11 - Conic Section
- Page 383 and 384: Class XI Chapter 11 - Conic Section
- Page 385 and 386: Class XI Chapter 11 - Conic Section
- Page 387 and 388: Class XI Chapter 11 - Conic Section
- Page 389 and 390: Class XI Chapter 11 - Conic Section
- Page 391 and 392: Class XI Chapter 11 - Conic Section
- Page 393 and 394: Class XI Chapter 11 - Conic Section
- Page 395 and 396: Class XI Chapter 11 - Conic Section
- Page 397 and 398: Class XI Chapter 11 - Conic Section
- Page 399 and 400: Class XI Chapter 11 - Conic Section
- Page 401 and 402: Class XI Chapter 11 - Conic Section
- Page 403 and 404: Class XI Chapter 11 - Conic Section
- Page 405 and 406: Class XI Chapter 11 - Conic Section
- Page 407 and 408: Class XI Chapter 11 - Conic Section
- Page 409 and 410: Class XI Chapter 11 - Conic Section
- Page 411 and 412: Class XI Chapter 11 - Conic Section
- Page 413 and 414: Class XI Chapter 11 - Conic Section
- Page 415 and 416: Class XI Chapter 11 - Conic Section
- Page 417 and 418: Class XI Chapter 12 - Introduction
- Page 419 and 420: Class XI Chapter 12 - Introduction
- Page 421 and 422: Class XI Chapter 12 - Introduction
- Page 423 and 424: Class XI Chapter 12 - Introduction
- Page 425 and 426: Class XI Chapter 12 - Introduction
- Page 427 and 428:
Class XI Chapter 12 - Introduction

- Page 429 and 430:
Class XI Chapter 12 - Introduction

- Page 431 and 432:
Class XI Chapter 13 - Limits and De

- Page 433 and 434:
Class XI Chapter 13 - Limits and De

- Page 435 and 436:
Class XI Chapter 13 - Limits and De

- Page 437 and 438:
Class XI Chapter 13 - Limits and De

- Page 439 and 440:
Class XI Chapter 13 - Limits and De

- Page 441 and 442:
Class XI Chapter 13 - Limits and De

- Page 443 and 444:
Class XI Chapter 13 - Limits and De

- Page 445 and 446:
Class XI Chapter 13 - Limits and De

- Page 447 and 448:
Class XI Chapter 13 - Limits and De

- Page 449 and 450:
Class XI Chapter 13 - Limits and De

- Page 451 and 452:
Class XI Chapter 13 - Limits and De

- Page 453 and 454:
Class XI Chapter 13 - Limits and De

- Page 455 and 456:
Class XI Chapter 13 - Limits and De

- Page 457 and 458:
Class XI Chapter 13 - Limits and De

- Page 459 and 460:
Class XI Chapter 13 - Limits and De

- Page 461 and 462:
Class XI Chapter 13 - Limits and De

- Page 463 and 464:
Class XI Chapter 13 - Limits and De

- Page 465 and 466:
Class XI Chapter 13 - Limits and De

- Page 467 and 468:
Class XI Chapter 13 - Limits and De

- Page 469 and 470:
Class XI Chapter 13 - Limits and De

- Page 471 and 472:
Class XI Chapter 13 - Limits and De

- Page 473 and 474:
Class XI Chapter 13 - Limits and De

- Page 475 and 476:
Class XI Chapter 13 - Limits and De

- Page 477 and 478:
Class XI Chapter 13 - Limits and De

- Page 479 and 480:
Class XI Chapter 13 - Limits and De

- Page 481 and 482:
Class XI Chapter 13 - Limits and De

- Page 483 and 484:
Class XI Chapter 13 - Limits and De

- Page 485 and 486:
Class XI Chapter 13 - Limits and De

- Page 487 and 488:
Class XI Chapter 13 - Limits and De

- Page 489 and 490:
Class XI Chapter 13 - Limits and De

- Page 491 and 492:
Class XI Chapter 14 - Mathematical

- Page 493 and 494:
Class XI Chapter 14 - Mathematical

- Page 495 and 496:
Class XI Chapter 14 - Mathematical

- Page 497 and 498:
Class XI Chapter 14 - Mathematical

- Page 499 and 500:
Class XI Chapter 14 - Mathematical

- Page 501 and 502:
Class XI Chapter 14 - Mathematical

- Page 503 and 504:
Class XI Chapter 14 - Mathematical

- Page 505 and 506:
Class XI Chapter 14 - Mathematical

- Page 507 and 508:
Class XI Chapter 15 - Statistics Ma

- Page 509 and 510:
Class XI Chapter 15 - Statistics Ma

- Page 511 and 512:
Class XI Chapter 15 - Statistics Ma

- Page 513 and 514:
Class XI Chapter 15 - Statistics Ma

- Page 515 and 516:
Class XI Chapter 15 - Statistics Ma

- Page 517 and 518:
Class XI Chapter 15 - Statistics Ma

- Page 519 and 520:
Class XI Chapter 15 - Statistics Ma

- Page 521 and 522:
Class XI Chapter 15 - Statistics Ma

- Page 523 and 524:
Class XI Chapter 15 - Statistics Ma

- Page 525 and 526:
Class XI Chapter 15 - Statistics Ma

- Page 527 and 528:
Class XI Chapter 15 - Statistics Ma

- Page 529 and 530:
Class XI Chapter 15 - Statistics Ma

- Page 531 and 532:
Class XI Chapter 15 - Statistics Ma

- Page 533 and 534:
Class XI Chapter 15 - Statistics Ma

- Page 535:
Class XI Chapter 15 - Statistics Ma