Question
Question: The line x + 2y + 3 = 0 and its conjugate with respect to the parabola y<sup>2</sup> = 4x are perpen...
The line x + 2y + 3 = 0 and its conjugate with respect to the parabola y2 = 4x are perpendicular to each other. The equation of the conjugate line is
A
2x - y + 1 = 0
B
2x - y + 5 = 0
C
2x - y + 10 = 0
D
2x - y - 10 = 0
Answer
2x - y - 10 = 0
Explanation
Solution
If the lines l1x+m1y+n1 =0, l2x+m2y+n2 =0 are conjugate lines w.r.to y2 = 4ax, then l1n2+l2n1 = 2am1m2.
Let the required line is 2x- y + λ =0
Given line is x+2y + 3= 0
By applying above condition
2 x 3 + 1.λ = 2 x 1.x-1 x 2
λ = 10
∴ Required equation is 2x – y – 10 = 0