Find the angle between the parabolas `y^2=4a x` and `x^2=4b y` at their point of intersection other than the origin.

Explanation

We have,


`y^{2}=4 a x text { and } x^{2}=4 b y `

`Rightarrow(frac{x^{2}}{4 b})^{2}=4 a x[because, x^{2}=4 b y Rightarrow y=frac{x^{2}}{4 b}] `

`Rightarrow x^{4}-64 a b^{2} x=0 `

`Rightarrow x(x^{3}-64 a b^{2})=0 `

`Rightarrow x=0, x=4 a^{1 / 3} b^{2 / 3}`


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