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Given two straight lines AB and AC whose equations are 3x + 4y = 5 and 4x – 3y = 15 respectively. Then the possible equation of line BC through (1, 2), such that ABC is isosceles, is L1 = 0 or L2 = 0, then answer the following questions Q-If L1 ax + by + c = 0 & L2 dx + ey + f = 0 where a, b, c, d, e, f I, and a, d > 0, then c + f = (Ans is 4)

Given two straight lines AB and AC whose equations are 3x + 4y = 5 and 4x – 3y = 15 respectively. Then the possible equation of line BC through (1, 2), such that ABC is isosceles, is L1 = 0 or L2 = 0, then answer the following questions
Q-If L1 ax + by + c = 0 & L2 dx + ey + f = 0 where a, b, c, d, e, f I, and a, d > 0, then c + f =                                  (Ans is 4)

Grade:12

1 Answers

Y RAJYALAKSHMI
45 Points
7 years ago
Equation of the line BC passing through (1,2) with slope ‘m’ is (y-2) = m(x-2)
Since ABC is isosceles, angle B = angle C.
using Cos(theta) formula for finding angle between the lines AB,BC & AC,BC, and equating them we get m = 1/7 or -7.
 
Substituting thes values in equation, we get x-7y + 13 = 0 & 7x + y – 9 = 0.
 
So c+f = 13-9=4 (ANS)
 
 

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