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

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