Question

If the curves y = 1 – ax² and y = x² are orthogonal, then find a.

Answer 1

Given curves are

y = 1 – ax² and y = x² ...(i)

⇒ dy/dx = –2ax; dy/dx = 2x

since the curves cut orthogonally, so

⇒ –2ax × 2x = –1

⇒ ax² = 1/4 ...(ii)

On solving (i) and (ii), we get, y = 5/4 = x²

Now, from (ii), we get,

a × 5/4 = 1/4

⇒ a = 1/5.