Review question

# Can we find the angle between these two tangents? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Ref: R5678

## Question

The point $P$ on the hyperbola $xy=c^2$ is such that the tangent to the hyperbola at $P$ passes through the focus of the parabola $y^2=4ax$. Find the coordinates of $P$ in terms of $a$ and $c$.

If $P$ also lies on the parabola, prove that $a^4=2c^4$, and calculate the acute angle between the tangents to the two curves at $P$.