How would I go about graphing the equation:
$\displaystyle 5x^2+9y^2=45$
?
There are two ways to think about this.
If you are using a graphing calculator, solve for y:
$\displaystyle y = \pm \sqrt{5 - \frac{5}{9}x^2}$
So graph the two pieces:
$\displaystyle y_1 = \sqrt{5 - \frac{5}{9}x^2}$
and
$\displaystyle y_2 = - \sqrt{5 - \frac{5}{9}x^2}$
Otherwise
$\displaystyle 5x^2+9y^2=45$
$\displaystyle \frac{x^2}{3^2} + \frac{y^2}{(\sqrt{5})^2} = 1$
is an ellipse with $\displaystyle a = 3 \text{ and }b = \sqrt{5}$ centered on (0, 0).
-Dan