The condition that the curves ax2+by2=1 anda1x2+b1y2=1 may cut each other orthogonally is

The given curves are ax2+by2=1 …………….(1) And a1x2+b1y2=1 …………..(2)From (1) 2ax+2bydydx=0⇒dydx=−axby=m1 (say)From (2) 2a1x+2b1ydydx=0⇒dydx=−a1xb1y=m2 (say)Since the curves are orthogonal , m1m2=−1 ∴(−axby)(−a1xb1y)=−1 ⇒aa1x2=−bb1y2 ……………(3)Solving (1) and (2) we get (a−a1)x2=(b1−b)y2..............(4) Dividing by (3), a−a1aa1=b−b1bb1