Show the condition that the curves `a x^2+b y^2=1` and `a^(prime)\ x^2+b^(prime)\ y^2=1` Should intersect orthogonally

Explanation

Let `P(x_{1}, y_{1})` be the point of intersection of the curves.


`therefore a_{1}^{2}+b y_{1}^{2}=1 text { and } a^{prime} x_{1}^{2}+b^{prime} y_{1}^{2}=1 `

`therefore a x_{1}^{2}+b y_{1}^{2}=a^{prime} x_{1}^{2}+b^{prime} y_{1}^{2} `

`therefore (a-a^{prime}) x_{1}^{2}=(b^{prime}-b) y_{1}^{2}`


Differentiating `a x^{2}+ by { }^{2}=1` w.r.t. x, we get


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