Question

Find the angle of intersection of the curves x2 = y and y2 = x.

Answer 1

The given curves are x2 = y and y2 = x

We have, x = x4

⇒ x (1 – x3) = 0

⇒ x = 0, 1

when x = 0, y = 0 and when x = 1, y = 1

So, the point of intersections are (0, 0), (1, 1)

At the point of intersection (0, 0)

Now, y = x2

⇒ dy/dx = 1m1 = ( dy/dx)(0,0) = 1

Now, consider the point of intersection (1, 1)

Now, consider the point of intersection (1, 1)