Review question

# Can we find where the normal is parallel to $y=x$? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Ref: R8939

## Suggestion

A curve has parametric equations $x=5a\sec\theta,\,y=3a\tan\theta$, where $-\frac{1}{2}\pi < \theta < \frac{1}{2}\pi$ and $a$ is a positive constant. Find the coordinates of the point on the curve at which the normal is parallel to the line $y=x$.

How can we find the derivative $\dfrac{dy}{dx}$ for this curve?

We want the normal to have the same gradient as $y=x$.

If we know the value of $\sin\theta$, how can we find the corresponding value of $\cos\theta$?