Given:

Curves y² = x ...(1)

& x² = y ...(2)

First curve is y² = x

Differentiating above w.r.t x,

⇒ 2y. = 1

⇒ m₁ ...(3)

The second curve is x² = y

⇒ 2x

⇒ m₂ = 2x ...(4)

Substituting (1) in (2),we get

⇒ x² = y

⇒ (y²)² = y

⇒ y⁴ – y = 0

⇒ y(y³ – 1) = 0

⇒ y = 0 or y = 1

Substituting y = 0 & y = 1 in (1) in (2),

x = y²

when y = 0,x = 0

when y = 1,x = 1

Substituting above values for m₁ & m_2,we get,

when x = 0,

m₁∞

when x = 1,

m₁

Values of m₁ is ∞ &

when y = 0,

m₂ = 2x = 2×0 = 0

when x = 1,

m₂ = 3x = 2×1 = 2

Values of m₂ is 0 & 2

when m₁ = ∞ & m₂ = 0

tanθ

tanθ

tanθ = ∞

θ = tan ^{– 1}(∞)

∴ tan ^{– 1}(∞)

θ

when m₁ & m₂ = 2

tanθ

tanθ

tanθ

θ = tan ^{– 1}()

θ≅36.86