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$If the curves \frac{x^{2}}{a^{2}} + \frac{y^{2}}{4} = 1 and y^{2} = 16 x intersect at right angle, then$

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Correct option is D

Clearly, the given curve intersect for a∈R−{0} For the parabola, dydx=8y. For the ellipse, dydx=−4xa2y For the curves to intersect orthogonally, 8y−4xa2y=−1⇒a2y2=32x⇒16a2x=32x⇒a2=2

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If the curves x2a2+y24=1 and y2=16x intersect at right angle, then

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$If the curves \frac{x^{2}}{a^{2}} + \frac{y^{2}}{4} = 1 and y^{2} = 16 x intersect at right angle, then$