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

Concept:

Equation of tangent at the point (x1, y1 ) of the curve y = f(x) is , where m = f'(x) is slope of the curve.

The line is passing through the point (x1, y1 ) if the point (x1, y1 ) is satisfying the equation of a line.

Calculator:

Given, equation of curve is x2y2 - 2x = 4(1 - y) 

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Equation of tangent at the point (x_1, y₁ ) of the curve y = f(x) is where m is slope of the curve.

Here (x1, y1 ) =  (2, -2) and m = 

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⇒ 7x - 6y = 26.

Hence, The equation of tangent at the point (2, -2) to the curve x2y2 - 2x = 4(1 - y) is  7x - 6y = 26.

Now, put the point (-2, -7) in The equation of tangent 7x - 6y = 26.

LHS = 7(-2) - 6(- 7) = 28

RHS = 26

⇒LHS  RHS

The tangent at the point (2, -2) to the curve x2y2 - 2x = 4(1 - y) does not pass through the point (-2, -7)