Class XI Chapter 10 – Straight Lines Maths ______________________________________________________________________________ Question 10: The line through the points (h, 3) and (4, 1) intersects the line 7x – 9y – 19 = 0. At right angle. Find the value of h. Solution 10: The slope of the line passing through points (h, 3) and (4, 1) is 13 2 m1 4h 4h 7 19 7 The slope of line 7x – 9y – 19 = 0 or y x is m2 . 9 9 9 It is given that the two lines are perpendicular. m1 m2 1 14 1 36 9h 14 36 9h 9h 36 14 22 h 9 Thus, the value of h is 22 9 Question **11**: Prove that the line through the point ( x 1 y 1 ) and parallel to the line Ax + By + C = 0 is A (x - x 1 ) + B (y - y 1 ) = 0. Solution **11**: A C The slope of line Ax + By + C = 0 or y x B B It is known that parallel lines have the same slope. A Slope of the other line = m=- B A is m=- B The equation of the line passing through point ( x 1 y 1 ) and having a slope A m=- B 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 y1 m( x x1) A y y1 - ( x x1) B B y y A( x x ) 1 1 A( x x ) B y y 0 1 1 Hence, the line through point ( x 1 y 1 ) and parallel to line Ax + By + C = 0 is A( xx ) B y y 0 1 1 Question 12: Two lines passing through the points (2, 3) intersects each other at an angle of 60 .If slope of one line is 2, find equation of the other line. Solution 12: It is given that the slope of the first line, m1 2 . Let the slope of the other line be m 2 . The angle between the two lines is 60 . m1 m2 tan60 1 mm 2m 2 2 2 3 1 2m2 2m2 3 1 2m2 2m 2m 2 2 3 or 3 12m2 12m2 m m or m m 3 1 2 2 3 1 2 2 2 2 2 2 3 2 3m m 2or 3 2 3m m 2 2 2 2 2 2 3 2 3 or m 2 3 1 2 3 1 3 2 3 1 m 2or 3 2 3 1 m 2 m Case 1 : 2 2 2 2 m 2 2 3 2 3 1 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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