What is the equation of tangent to the hyperbola
$2 x^{2} - 3 y^{2} = 6$ which is parallel to the line $y = 3 x + 4$ , is

$y = 3 x + 5$

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$y = 3 x - 5$

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$y = 3 x + 5 and y = 3 x - 5$

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None of the above

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Solution

The correct option is C
$y = 3 x + 5 and y = 3 x - 5$

We know that for any standard hyperbola
$\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1,$

the equation for tangent of slope 'm' will be , $y = m x \pm \sqrt{a^{2} m^{2} - b^{2}}$ .

Here the given hyperbola is, $2 x^{2} - 3 y^{2} = 6$

And slope of tangent =3

$∴$ required equation of tangent

$y = 3 x \pm \sqrt{3 \times 9 - 2} = 3 x \pm 5$ .

Hence option (c) is correct.

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Similar questions

2 x^{2} - 3 y^{2} = 6

2 x^{2} - 3 y^{2} = 6

y = 3 x + 4

What is the equation of tangent to the hyperbola
$2 x^{2} - 3 y^{2} = 6$ which is parallel to the line $y = 3 x + 4$ , is

x^{2} - 3 y^{2} = 9

y = 3 x + 5.

Equation of the line passing through $(1, 2)$ and parallel to the line $y = 3 x - 1$ is

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