If the chord y = mx + c subtends a right angle at the vertex of the parabola y^2 = 4ax, then the value of c is

Q: If the chord y = mx + c subtends a right angle at the vertex of the parabola y2 = 4ax, then the value of c is

(A) – 4am

(B) 4am

(C) –2am

(D) 2am

Sol. The combined equation of the lines joining the origin (vertex) to the points of intersection of y2 = 4ax and y = mx + c is

$\large y^2 = 4 a x (\frac{y-mx}{c})$

⇒  cy2 – 4 a x y + 4 a m x2 = 0.

This represents a pair of perpendicular lines,

therefore c + 4am = 0 i.e. c = – 4am

Hence (A) is the correct answer.