Class XI Chapter 10 – Straight Lines Maths ______________________________________________________________________________ mc 1 2 m2c1 c2 c1 m3 c3 m1 m2 m1 m2 mc 1 2 m2c1 m3c 2 m3c 1 c3m1 c3m2 m1 m2 m1 m2 mc m c m c m c c m c m 0 1 2 2 1 3 2 3 1 3 1 3 2 0 m c c m c c m c c m c c m c c m c c 1 2 3 2 3 1 3 1 2 Hence, 0 1 2 3 2 3 1 3 1 2 Question **11**: Find the equation of the line through the points (3, 2) which make an angle of 45 with the line x – 2y = 3. Solution **11**: Let the slope of the required line be m 1 . The given line can be written as y = 1 x 3 , which is of the form y= mx + c 2 2 1 Slope of the given line = m2 2 It is given that the angle between the required line and line x – 2y = 3 is 45 . We know that if is the acute angle between lines l 1 and l 2 with slopes m1and m 2 respectively, then m2 m1 tan = 1 mm 1 2 m m tan 45 = 2 1 1 mm 1 1 1 m1 2 m1 1 2 12m1 2 2 m1 2 1 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 ______________________________________________________________________________ 12m 1 2 m 1 1 12m1 1 2 m1 12m 12m 1 1 1 or 1 2m1 2m1 2 m1 12m1 or 2 m1 1 2m1 1 m1 or m1 3 3 Case I: m1 3 The equation of the line passing through (3,2) and having a slope of 3 is: y-2=3(x-3) y-2=3x-9 3x-y=7 1 Case II: m1 3 1 The equation of the line passing through (3,2) and having a slope of is : 3 1 y-2= ( x 3) 3 3y6 x3 x3y9 Thus, the equations of the line are 3x-y=7 and x3y9. Question 12: Find the equation of the line passing through the point of intersection of the line 4x + 7y – 3 = 0 and 2x – 3y + 1 = 0 that has equal intercepts on the axes. Solution 12: Let the equation of the line having equal intercepts on the axes be x y 1 a a Or x+y=a ...(1) On solving equations 4x + 7y – 3 = 0 and 2x – 3y + 1 = 0, we obtain 1 5 x= and y 13 13 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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