Question

Let $\alpha_{1}$ and $\alpha_{2}$ be the ordinates of two points $A$ and $B$ on a parabola $y^{2}=4 a x$ and let $\alpha_{3}$ be the ordinate of the point of intersection of its tangents at $A$ and $B$. Then, $\alpha_{3}-\alpha_{2}=$

• A. $\alpha_{3}-\alpha_{4}$
• B. $\alpha_{3}+\alpha_{1}$
• C. $\alpha_{1}$
• D. $\alpha_{1}-\alpha_{3}$

Answer 1

Answer: (D)

Ordinate of point of intersection of tangents at $A$ and $B$ whose ordinates are $\alpha_{1}$ and $\alpha_{2}$ is $\frac{\alpha_{1}+\alpha_{2}}{2}$
So, $\alpha_{3}=\frac{\alpha_{1}+\alpha_{2}}{2}$
$2 \alpha_{3}=\alpha_{1}+\alpha_{2}$
$\Rightarrow \alpha_{3}-\alpha_{2}=\alpha_{1}-\alpha_{3}$