First slide

Parabola

Question

$Tangents are drawn from any point on the line x + 4 a = 0 to the parabola y^{2} = 4 a x . Then the angle subtended by$
$chord of contact at the vertex is$

Moderate

A

$30^{o}$
B

$45^{o}$
C

$60^{o}$
D

$90^{o}$

Solution

$Let P (a t_{1}^{2}, 2 a t_{1}) and Q (a t_{1}^{2}, 2 a t_{2}) be the points of contact for tangents drawn from any point on the line x + 4 a = 0$
$Their point of intersection will be on this line. Therefore,$
$\begin{array}{c} a t_{1} t_{2} + 4 a = 0 \\ o r t_{1} t_{2} = - 4 \end{array}$
This is also the condition for chord PQ to subtend a right angle
at the vertex.

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