Problem

Let the line

lx + my = 1

cut the parabola

y^2 = 4ax

in the points A and B. Normals at A and B meet at point C. Normal from C other than these two meet the parabola at D, then the coordinate of D are a.

(a, 2a)

\left( \frac{4am}{l^2}, \frac{4a}{l} \right)

\left( \frac{2am^2}{l^2}, \frac{2a}{l} \right)

\left( \frac{4am^2}{l^2}, \frac{4am}{l} \right)