If the curves x2a2+y2b2=1 and x2α2+y2β2=1 cut each other orthogonally,
Slope of I=−b2xa2y=m1 (say),
And slope of II =β2α2y=m2(say)∴m1m2=1∴b2β2x2=a2α2y2
and x2a2+y2b2−1=0
x2α2−y2β2−1=0⇒x2(1a2−1α2)=−y2(1b2−1β2)
From Eqs. (i) and (ii)
⇒1a2−1α2b2β2=−(1b2−1β2)a2α2⇒α2+β2=a2+b2
note: remember it as formula