Question

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

• A. $y=3x+5$
• B. $y=3x-5$
• C. $y=3x+5\text{and}y=3x-5$
• D. None of the above

Answer 1

The correct option is C

$y=3x+5\text{and}y=3x-5$

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 , $y=mx\pm \sqrt{a^2{m}^2-b^2}$.

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

And slope of tangent =3

$\therefore$ required equation of tangent

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

Hence option (c) is correct.