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: