Mathematics

Problem

If the tangent drawn at point

(\lambda^2, 2\lambda)

on the parabola

y^2 = 4x

is same as the normal drawn at a point

(\sqrt{5} \cos \theta, 2 \sin \theta)

on the ellipse

4x^2 + 5y^2 = 20

. Find the values of

\lambda

and

\theta