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

\(c^4=32a^4\) and

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

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

\(c^4=32a^4\) and

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