Q. 8 B5.0( 1 Vote )

Find the condition for the following set of curves to interest orthogonally.

and

Answer :

Given:


Curves 1 ...(1)


& 1 ...(2)


First curve is 1


Differentiating above w.r.t x,


. = 0


.




m1 ...(3)


Second curve is 1


Differentiating above w.r.t x,


. = 0


.




m1 ...(4)


When m1 & m2 =


Since ,two curves intersect orthogonally,



× = – 1


× = – 1


...(5)


Now equation (1) – (2) gives



x2() – y2() = 0


x2() = y2()





Substituting from equation (5),we get



– 1


( – 1)(A2 – a2) = (B2 – b2)


a2 – A2 = B2 – b2


a2 + b2 = B2 + A2


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