Question
If the curve αx2 + βy2 = 1 and α' x2 + β'y2 = 1 intersect orthogonally, prove that (α – α') β β') = (β – β') α α'.
Solution
The equations of two curves are
...(1)
and 
...(2)
Let curves (1) and (2) intersect at 
...(3)
and 
...(4)
Subtracting (4) from (3), we get,
At 
Similarly for second curve,
Since the two curves (1) and (2) intersect orthogonally,
