Find the condition for the following set of curves to interest orthogonally.
and xy = c2
Given:
Curves 
1 ...(1)
& xy = c2 ...(2)
First curve is 
1
Differentiating above w.r.t x,
⇒ 
.
= 0
⇒ 
.
⇒ 
⇒ 
⇒ m1
...(3)
Second curve is xy = c2
⇒ ⇒ 1×y + x.
= 0
⇒ x.
= – y
⇒ m2
...(4)
When m1
& m2 = 
Since ,two curves intersect orthogonally,
⇒ 
×
= – 1
⇒ 
= 1
⇒ ∴ a2 = b2
8