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?

  1. 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?