The tangent at the point (4 cosφ, 16/√11 sinφ) to the ellipse 16x^2 + 11y^2 = 256 is also a tangent to the circle

Question

The tangent at the point \(\left(4cos\phi, \frac{16}{\sqrt {11}}sin\phi\right)\) to the ellipse 16x² + 11y² = 256 is also a tangent to the circle x² + y² – 2x = 15, find the value of φ.

Answer 1

The value of φ is \(\pm \frac \pi6\).