Question

The required point is?

Answer 1

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).