The curves \(y^2=4ax\) and \(xy=c^2\) intersect at right angles. Prove that (i) \(c^4=32a^4\)

What do the curves \(y^2=4ax\) and \(xy=c^2\) look like? Could we sketch a diagram?

If the curves meet at \((p,q)\), what are the gradients of the curves there?

What condition on the slopes of two lines corresponds to them being at right angles?

- if the tangent and normal to either curve at the point of intersection meet the \(x\)-axis at \(T\) and \(G\), then \(TG=6a\).

What are the equations of the tangent and normal?

Where do these lines meet the \(x\)-axis?