Q8 of 149 Page 16

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


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