(A) Any line passing through the intersection of the lines 2x - 5y + 3 = 0 and x - 3y - 7 = 0 is of the form
This line is perpendicular to the line
Hence, the required line is
Answer: (A) → (q)
(B) The required line equation is of the form (3x - 2y + 10) + λ(4x + 3y - 7) = 0.This passes through the point (2, 1) which implies that
[3(2) -2(1) + 10] λ(8 + 3 - 7) = 0
14 + 4λ
λ = -7/2
Hence the required line is
Answer: (B) → (q)
(C) Let the line be
x/a + y/b = 1
Therefore
-2/a - 4/b = 1
or 4a + 2b = -ab ....(1)
and a + b = 3 ....(2)
Solving Eqs. (1) and (2), we have a = -1, b = 4 or a = 6 3 , ., b = -3
Answer: (C) → (r), (t)
(D) The slope of BC is
7 - 4/2 - 3 = -3
Hence, the equation of the line passing through A(1, 2) and perpendicular to the line BC is
y - 2 = 1/3(x - 1)
x - 3y + 5 = 0
Answer: (D) → (s)