Q95 / 160 · AP EAMCET 2018 (22 Apr Shift 2) · Mathematics

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
    $\alpha_3-\alpha_1$
  • B
    $\alpha_3+\alpha_1$
  • C
    $\alpha_1$
  • Correct answer
    D
    $\alpha_1-\alpha_3$

Solution

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, $$ \begin{aligned} \alpha_3 & =\frac{\alpha_1+\alpha_2}{2} \\ 2 \alpha_3 & =\alpha_1+\alpha_2 \Rightarrow \alpha_3-\alpha_2=\alpha_1-\alpha_3 . \end{aligned} $$

Hence, the correct answer is option: 'D'.

More Parabola Questions