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The equation of the tangent to the hyperbola \mathrm{2 x^{2}-3 y^{2}=6} which is parallel to the line \mathrm{y=3 x+4} is

Option: 1

\mathrm{y=3 x+5}


Option: 2

\mathrm{y=3 x-5}


Option: 3

\mathrm{y=3 x+5\: and \: y=3 x-5}


Option: 4

none of these


Answers (1)

best_answer

The equation of the tangent to \mathrm{\frac{x^{2}}{16}-\frac{y^{2}}{b^{2}}=1} is

\mathrm{y=m x \pm \sqrt{a^{2} m^{2}-b^{2}}}, where \mathrm{m} is the slope of the tangent.

Here \mathrm{\mathrm{a}^{2}=3, \mathrm{~b}^{2}=2\: and \: \mathrm{m}=3}.

Therefore the equations of the tangents are \mathrm{y=3 x \pm \sqrt{27-2}\: or \: y=3 x \pm 5}
 

Posted by

avinash.dongre

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