show that the condition that the curves ax2+by2=1 and a'x2+b'y2=1 should intersect orthogonally (at900) 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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