Class XI Chapter 10 – Straight Lines Maths ______________________________________________________________________________ 3b 9 1 4a 4 3b 9 4a 4 4a 3b 5 ... 1 Point (a, b) lies on line 3x – 4y = 16 . 3a – 4b = 16 …(2) On solving equations (1) and (2), we obtain 68 49 a and b = - 25 25 Thus, the required coordinates of the foot of the perpendicular are 68 49 ,- 25 25 Question 15: The perpendicular from the origin to the line y = mx + c meets it at the point (-1, 2). Find the values of m and c. Solution 15: The given equation of line is y = mx + c. It is given that the perpendicular from the origin meets the given line at (-1, 2). Therefore, the line joining the points (0, 0) and (-1, 2) is perpendicular to the given line. slope of the line joining (0, 0) and (-1, 2) = 2 1 = -2 The slope of the given line is m. m – 2 = -1 [The two lines are perpendicular] m = 1 2 Since points (-1, 2) lies on the given line, it satisfies the equation y = mx + c. 2 = m(-1) + c 2 = 2 + 1 2 (-1) + c c = 2 + 1 2 = 5 2 Thus, the respective values of m and c are 1 2 and 5 2 . Printed from Vedantu.com. Register now to book a Free LIVE Online trial session with a Top tutor.

Class XI Chapter 10 – Straight Lines Maths ______________________________________________________________________________ Question 16: If p and q are the lengths of perpendicular from the origin to the lines x cos - y sin = k cos 2 2 2 2 and x sec +y cosec = k, respectively, prove that p 4q k Solution 16: The equation of given lines are x cos - y sin = k cos 2 …(1) x sec +y cosec = k …(2) The perpendicular distance (d) of a line Ax + By + C = 0 from a point x x is given by d Ax By C 1 1 2 2 A B On comparing equation (1) to the general equation of line i.e., Ax + By + C = 0, we obtain A = cos , B = -sin , and C = -k cos 2 . It is given that p is the length of the perpendicular from (0, 0) to line (1). A(0) B 0 C C kcos2 p kcos2 …(3) 2 2 2 2 2 2 A B A B cos sin On comparing equation (2) to the general equation of line i.e., Ax + By + C = 0, we obtain A = sec , B = cosec , and C = -k. It is given that q is the length of the perpendicular from (0, 0) to line (2). A(0) B 0 C C k q 2 2 2 2 2 2 A B A B sec cos ec From (3) and (4), we have 2 2 2 k p 4q k cos2 4 2 2 sec cos ec 2 2 2 4k k cos 2 2 2 sec cos ec 4k 2 2 2 k cos 2 1 1 2 2 cos sin 4k sin cos 2 2 sin cos 2 2 2 k cos 2 2 2 4k 2 2 2 k cos 2 1 2 2 k sin cos cos 2 4k sin cos 2 2 2 2 2 2 1, 2 …(4) 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: 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 and 376: Class XI Chapter 11 - Conic Section
- Page 377 and 378: 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