The required point is?

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1 Answer
Mar 15, 2018

Answer is (4).

Explanation:

Let us find the slope of tangent on curve x^2y^2-2x=4(1-y) at point (2,-2), which is given by its derivative at the point. Derivative is given by

2xy^2+2x^2y(dy)/(dx)-2=-4(dy)/(dx)

i.e. (dy)/(dx)=(2(1-xy^2))/(2(x^2y+2))=(2(1-2*(-2)^2))/(2(2^2*(-2)+2))=7/6

and equation of tangent is y+2=7/6(x-2) or 6y-7x+26=0 or y=(7x-26)/6

It can be easily seen that while (4,1/3),(8,5) and (-4,-9) lie on tangent, (-2,-7) does not lie on tangent.

Hence answer is (4).