Q. 55.0( 3 Votes )

Show that the curves 2x = y2 and 2xy = k cut at right angles, if k2 = 8.

Answer :

Given:


Curves 2x = y2 ...(1)


& 2xy = k ...(2)


We have to prove that two curves cut at right angles if k2 = 8


Now ,Differentiating curves (1) & (2) w.r.t x, we get


2x = y2


2 = 2y.



m1 ...(3)


2xy = k


Differentiating above w.r.t x,


2(1×) = 0


= 0



m2 ...(4)



Since m1 and m2 cuts orthogonally,


×1


1


x = 1


Now , Solving (1) & (2),we get,


2xy = k & 2x = y2


(y2)y = k


y3 = k


y


Substituting y in 2x = y2,we get,


2x = ()2


2×1


2


23


8


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