Question

The tangent at the point (2, −2) to the curve, x²y² – 2x = 4(1 – y) does not pass through the point

(A) (−2, −7)

(B) (−4, −9)

(C) (4, 1/3)

(D) (8, 5)

Answer 1

Answer is (A) (−2, −7)

The given curve is

x²y² – 2x = 4(1 – y)

Differentiating this equation, we get

The equation of tangent is given by

(y - y₁) = dy/dx|_{(x, y)} (x - x₁)

Here, x₁ = 2 and y₁ = 2. Therefore

y - (-2) = 7/6(x - 2)

All the given points (8, 5), (−4, −9) and (4, 1/3) satisfy the equation except the point (−2, −7):

7x - 6y|_{(-2, -7)} = 28

Therefore, the tangent at point (2, −2) of the given curve does not pass through the point (−2, −7).