Show that the curves `x=y^2` and `x y=k` cut at right angles, if `8k^2=1` .

Explanation

`x=y^2 ; xy=k`


Let the curves cut each other at `(a, b)`

`a=b^{2} ; a b=k `

`x=y^{2} quad ; x y=k `

`1=2 y frac{d y}{d x} ; quad x frac{d y}{d x}+y=0 `

`frac{d y}{d x}=frac{1}{2} y ; quad frac{d y}{d x}=frac{-y}{x}`


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