Parabola

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Question

$y = x + 2 is any tangent to the parabola y^{2} = 8 x . The ordinate of the point P on this tangent such that the other tangent$
$from it which is perpendicular to it is$

Moderate

Solution

$Clearly P is the point of intersection of two perpendicular tangents to the parabola y^{2} = 8 x .$
$Here, 4 a = 8 or a = 2 Hence P must lie on the directrix$
$\begin{array}{l} x + a = 0 or x + 2 = 0 \\ ∴ x = - 2 . Hence the point is (- 2, 0) . \end{array}$

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