Tangents are drawn to the ellipse $\frac{x^{2}}{36} + \frac{y^{2}}{9} = 1$ from any point on parabola $y^{2} = 4 x$ . The corresponding chord of contact will touch a parabola, whose equation is

y^{2} + 4 x = 0

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y^{2} = 4 x

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4 y^{2} + 9 x = 0

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y^{2} + 9 x = 0

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Solution

The correct option is A $4 y^{2} + 9 x = 0$
Given equation of ellipse is
$\frac{x^{2}}{36} + \frac{y^{2}}{9} = 1$
Given equation of parabola is $y^{2} = 4 x$
Let $P (t^{2}, 2 t)$ be a point on the parabola from where tangents to ellipse are drawn.
Equation of tangent to ellipse is
$\frac{x t^{2}}{36} + \frac{2 y t}{9} = 1$
$x t^{2} + 8 y t - 36 = 0$
which is the corresponding chord of contact.
Since, it touches parabola
$D = 0$
$64 y^{2} + 4 \times 36 \times x = 0$
$4 y^{2} + 9 x = 0$

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