How do you write the hyperbola 36x^2-9y^2=324 in standard form?

1 Answer
Oct 9, 2016

${\left(6 x\right)}^{2} / {18}^{2} - {\left(3 y\right)}^{2} / {18}^{2} = 1$

Explanation:

Target form is $\frac{{\left(y - k\right)}^{2}}{a} ^ 2 - \frac{\left(x - {h}^{2}\right)}{b} ^ 2 = 1$

Notice that $36 = {6}^{2} \text{; "9=3^2"; } 324 = {18}^{2}$

So we can write:

${\left(6 x\right)}^{2} / {a}^{2} - {\left(3 y\right)}^{2} / {b}^{2} = {18}^{2}$

So $h \text{ and } k = 0 \leftarrow$ symmetrical about the origin

Divide both sides by ${18}^{2}$

${\left(6 x\right)}^{2} / {18}^{2} - {\left(3 y\right)}^{2} / {18}^{2} = 1$