Equations of the tangents to the hyperbola $2 x^{2} - 3 y^{2} = 6$ which are parallel to the line $y = 3 x + 4$

y = 3 x \pm 5

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y = 3 x \pm 6

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y = 3 x \pm 7

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None of these

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Solution

The correct option is B $y = 3 x \pm 5$
$2 x^{2} - 3 y^{2} = 6$

$\frac{x^{2}}{3} - \frac{y^{2}}{2} = 1$

The line $y = m x + c$ will be

tang. to hyperbola $\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1$ only

$| c | = \sqrt{a^{2} m^{2} - b^{2}}$

Given line $y = 3 x + 4$

Slope $= m = 3$

$| c | = \sqrt{3 \times {(3)}^{2} - 2}$

$= \sqrt{27 - 2} = \sqrt{25} = 5$

Slope $= y = m x + c$

$y = 3 x \pm 5$

Suggest Corrections

Similar questions

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

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

3 x^{2} - 4 y^{2} = 12

4 x^{2} + 3 y^{2} = 5

y = 3 x + 7

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

y = 3 x + 5.

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