show that the condition that the curves ax^{2}+by^{2}=1 and a'x^{2}+b'y^{2}=1 should intersect orthogonally (at90^{0}) such that 1/a-1/b=1/a'-1/b'

Let the point of intersection of the curves be , so this point must satisfy both the equations

So now equations become as shown below:

Solving (1) and (2) for we get:

Differentiating the given equations w.r.t *x* we get:

At point the slopes would be:

Now the curves intersect orthogonally at point if the product of slopes=-1, so it means:

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