Equation of a tangent to the hyperbola $5 x^{2} - y^{2} = 5$ and which passes through an external point $(2, 8)$ is

3 x - y + 2 = 0

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3 x + y - 14 = 0

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23 x - 3 y - 22 = 0

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3 x - 23 y + 178 = 0

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Solution

The correct options are
A $3 x - y + 2 = 0$
C $23 x - 3 y - 22 = 0$
Equation of hyperbola is $\frac{x^{2}}{1} - \frac{y^{2}}{5} = 1$
Equation of the tangent is $y = m x \pm \sqrt{m^{2} - 5}$
Since, it passes through $(2, 8)$
$\Rightarrow (8 - 2 m)^{2} = m^{2} - 5$
$\Rightarrow 3 m^{2} - 32 m + 69 = 0$
$\Rightarrow m = 3 or \frac{23}{3}$

$∴$ Equations of tangent are
$3 x - y \pm 2 = 0$ and $23 x - 3 y \pm 22 = 0$

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Similar questions

(2, 8)

5 x^{2} - y^{2} = 5

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