Question

Angle between the parabolas y² = 4(x−1) and x² + 4(y−3) = 0 at the common end of their latus rectum, is

Answer 1

End points of latus rectum of y² = 4(x − 1) are (2, 2) and (2, −2)

End points of latus rectum of x² = −4(y − 3) are (2, 2) and (−2, 2)

So, the common point is (2, 2)

y² = 4(x − 1)

\(\therefore \frac{dy}{dx} = \frac 2y\)

Slope of tangent at (2, 2) = m₁ = \(\frac 22 \) = 1

x² = −4(y − 4)

\(\therefore \frac{dy}{dx} = \frac x{-2}\)

Slope of tangent at (2, 2) = m₂ = \(\frac 22 \) = 1

m₁m₂ = 1