Question

Prove that the curves x = y and xy = k cut at right angles if 8k2 = 1.

Answer 1

The given curves are x = y2 and x y = k

On solving we get, y = k1/3, x = k2/3

So, the point of intersection is P(k2/3, k1/3)

Now, y2 = x

⇒ 2y(dy/dx) = 1

since the given curves cut at right angles, so