Find the condition for the two concentric ellipses `a_1x^2+\ b_1y^2=1\ a n d\ a_2x^2+\ b_2y^2=1` to intersect orthogonally.

Explanation

Given curves are
`a x^{2}+b y^{2}=1 and a^{\prime} x^{2}+b^{\prime} y^{2}=1 `


`\Rightarrow 2 a x+2 b y \frac{d y}{d x}=0 ; 2 a^{\prime} x+2 b^{\prime} y \frac{d y}{d x}=0 `



`\Rightarrow \frac{d y}{d x}=-\frac{a x}{b y} ; \frac{d y}{d x}=-\frac{a^{\prime} x}{b^{\prime} y}`


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