Ex 10.3, 12 - Chapter 10 Class 11 Straight Lines

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Ex 10.3, 12 Two lines passing through the point (2, 3) intersects each other at an angle of 60 . If slope of one line is 2, find equation of the other line. We know that Angle between 2 lines be tan =|( _2 _1)/(1 + _2 _1 )| Here m1 = Slope of one line = 2 = 60 (given) We need to find m2 Putting the values tan 60 = |( _2 2)/(1 + 2 _2 )| 3 = |( _2 2)/(1 + 2 _2 )| |( _2 2)/(1 + 2 _2 )|= 3 ( _2 2)/(1 + 2 _2 ) = 3 So, ( _2 2)/(1 + 2 _2 ) = 3 and ( _2 2)/(1 + 2 _2 ) = 3 We know that equation of a line passing through (x1, y1) & having slope m is (y y1) = m(x x1) Equation of a line passing through (2, 3) & having slope ( + )/( ) is (y 3) = ( (2 + 3))/(1 2 3) (x 2) (1 2 3)(y 3) = (2 + 3)(x 2) 1(y 3) 2 3(y 3) = 2(x 2) + 3(x 2) y 3 2 3y + 6 3 = 2x 4 + 3x 2 3 y 2 3y 4x 3x = 6 3 2 3 4 + 3 y (1 2 3) x( 3 + 2) = 1 8 3 1 + 8 3 = x( 3 + 2) + y (2 3 1) ( 3 + 2)x + (2 3 1)y = 1 + 8 3 Equation of a line passing through (2, 3) & having slope ( )/( + ) is (y 3) = (2 3)/(2 3 + 1)(x 2) (2 3 + 1) (y 3) = (2 3) (x 2) 2 3 (y 3) + 1 (y 3) = 2(x 2) 3(x 2) 2 3 (y 3) + 1 (y 3) = 2(x 2) 3(x 2) 2 3y 6 3 + y 3 = 2x 4 3x + 2 3 2 3y + y 6 3 3 = 2x 3x 4 + 2 3 (2 3 + 1)y 6 3 3 = (2 3)x 4 + 2 3 (2 3 + 1)y = ( 3 2)x 4 + 2 3 + 6 3 + 3 (2 3 + 1)y + ( 3 2)x = 2 3 + 6 3 4 + 3 ( 3 2)x + (2 3 + 1)y = 8 3 1 Hence the equation of lines is ( 3 + 2)x + (2 3 1)y = 1 + 8 3 or ( 3 2)x + (2 3 + 1)y = 8 3 1