Class XI Chapter 10 – Straight Lines Maths ______________________________________________________________________________ Question 4: Find the equation of the line which passes through 2,2 3 and is inclined with the x-axis at an angle of 75 Solution 4: The slope of the line that inclines with the x-axis at an angle of 75 is m = tan 75 1 3 1 1 tan45 tan30 3 3 3 1 m tan(45 30 ) 1tan45 .tan30 1 **11**. 3 1 3 1 3 3 We know that the equation of the line passing through point x y , whose slope is m, is y y mx x 0 0 . Thus, if a line passes through 2,2 3 and inclines with the x-axis at an angle of 75 , then the equation of the line is given as 31 y x 31 2 y2 3 3 1 3 1 x2 y 3 1 2 3 3 1 x 3 1 2 3 1 3 1 x 3 1 y 2 3 26 2 3 3 1 x 3 1 y 4 3 4 i. e., 3 1 x 3 1 y 4 3 1 0, 0 Question 5: Find the equation of the line which intersects the x-axis at a distance of 3 units to the left of origin with slope -2. Solution 5: It is known that if a line with slope m makes x-intercept d, then the equation of the line is given as Y = m (x – d) For the line intersecting the x-axis at a distance of 3 units to the left of the origin, d = -3. The slope of the line is given as m = -2 Thus, the required equation of the given line is 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 ______________________________________________________________________________ Y = -2 [x – (-3)] Y = -2x – 6 i.e., 2x + y + 6 = 0 Question 6: Find the equation of the line which intersects the y-axis at a distance of 2 units above the origin and makes an angle of 30 with the positive direction of the x-axis. Solution 6: It is known that if a line with slope m makes y – intercept c, then the equation of the line is given as Y = mx + c 1 Here, c = 2 and m = tan 30 = 3 Thus, the required equation of the given line is 1 y x2 3 x y 2 3 3 3yx2 3 i.e.,x- 3y 2 3 0 Question 7: Find the equation of the line which passes through the points (-1, 1) and (2, -4). Solution 7: , and It is known that the equation of the passes through points y y y y x x 2 1 1 1 x2 x2 Therefore, the equation of the line passing through the points (-1, 1) and (2, -4) is 41 ( y1) x1 21 5 ( y1) x1 3 x y x y 1 1 , is 2 2 Printed from Vedantu.com. Register now to book a Free LIVE Online trial session with a Top tutor.

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Class XI Chapter 12 - Introduction

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