Question

Let the line lx + my = 1 cut the parabola y2 = 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)
• B. $\left( \frac{4am}{\mathcal{l}^{2}},\frac{4a}{\mathcal{l}} \right)$
• C. $\left( \frac{2am^{2}}{\mathcal{l}^{2}},\frac{2a}{\mathcal{l}} \right)$
• D. $\left( \frac{4am^{2}}{\mathcal{l}^{2}},\frac{4am}{\mathcal{l}} \right)$

Answer 1

Answer: (D)

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

Answer 2

Three points A, B and D are co-normal.

y2 – 4a $\left( \frac{1 - my}{\mathcal{l}} \right)$ = 0

y1 + y = $\frac{- 4am}{\mathcal{l}}$

̃ y1 + y2 + y3 = 0

̃ y1 =$\frac{4am}{\mathcal{l}}$