Straight lines 3 x + 4 y = 5 and 4 x - 3 y = 15 intersect at the point A . If point B and C are chosen on these two lines such that A B = A C , then the possible equation of the line B C passing through the point 1 , 2 is

Step-by-step solution

The given straight lines are 3 x + 4 y = 5 and 4 x - 3 y = 15 . Clearly, these straight lines are perpendicular to each other m 1 m 2 = - 1 and intersect at A . Now, B and C are points on these lines such that A B = A C and B C passes through 1 , 2 . From figure it is clear that ∠ B = ∠ C = 45 ° Let slope of B C be m . Then, tan 45 ° = m + 3 4 1 - 3 4 m ⇒ ± 1 = 4 m + 3 4 - 3 m 4 m + 3 = ± 4 - 3 m 4 m + 3 = 4 - 3 m or 4 m + 3 = - 4 + 3 m m = 1 7 or m = - 7 Hence, equation of B C