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Point Form of Tangent: Hyperbola

The equation ...

Question

The equation of the tangent to the conic $x^{2} - y^{2} - 8 x + 2 y + 11 = 0$ at $(2, 1)$ is:

y = 1

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x + y = 3

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x = 2

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2 x - y = 3

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Solution

The correct option is C $x = 2$
The equation of tangent to curve $x^{2} - y^{2} - 8 x + 2 y + 11 = 0$
at $(2, 1)$ is $T = 0$
$\Rightarrow 2 x - y - 4 (x + 2) + (y + 1) + 11 = 0$
$\Rightarrow x = 2$

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