Question

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

Answer 1

Solving the given equations, we have y² = x and x² = y ⇒ x⁴ = x or x⁴ – x = 0

⇒ x (x³ – 1) = 0 ⇒ x = 0, x = 1

Therefore, y = 0, y = 1

i.e. points of intersection are (0, 0) and (1, 1)

At (0, 0), the slope of the tangent to the curve y² = x is parallel to y-axis and the tangent to the curve x² = y is parallel to x-axis.

⇒ angle of intersection = π/2

At (1, 1), slope of the tangent to the curve y² = x is equal to 1/2 and that of x² = y is 2.