# What is the equation of hyperbola

Given that the equation of asymptotes to the hyperbola be:

$y=\pm\frac{3x}{2}$ and $b=4$

How to find the equation of hyperbola?

I know that asymtotes have the equation $y=\pm\frac{bx}{a}$, comparing and solving we get $a=\frac{8}{3}$

But in the exercise there are two answers given :

$\frac{9x^2}{64}-\frac{y^2}{16}=1$ and $\frac{y^2}{36}-\frac{x^2}{16}=1$.

How are there tw0 answers. Please Help. Thanks.

• I believe you mean the asymptotes to be $y= \pm \frac 32 x$: you left out the $x$. – Rory Daulton Sep 1 '14 at 14:35
• It could be either $$\dfrac{b}{a} = \dfrac{3}{2}$$ or $$\dfrac{a}{b} = \dfrac{3}{2}$$ – rrr Sep 1 '14 at 14:37
• @user172209 i dont understand ?? – Shobhit Sep 1 '14 at 14:38
• @RoryDaulton thanks – Shobhit Sep 1 '14 at 14:38
• How do you know whether the hyperbola is horizontal or vertical ? – rrr Sep 1 '14 at 14:39

## 1 Answer

HINT

If the given asymptotes are for horizontal hyperbola $$\dfrac{b}{a} = \dfrac{3}{2}$$

otherwise for vertical :

$$\dfrac{a}{b} = \dfrac{3}{2}$$