Answer
$y = + \frac{3}{2}\sqrt{(4 - x^{2})}$ or $y = - \frac{3}{2}\sqrt{(4 - x^{2})}$.
Work Step by Step
$9x^{2} + 4y^{2} = 36$
Thus, $ 4y^{2} = 36 - 9x^{2}$
$4y^{2} = 9(4 - x^{2})$
$y^{2} = \frac{9}{4}(4 - x^{2})$
Thus, $y = + \frac{3}{2}\sqrt{(4 - x^{2})}$ or $y = - \frac{3}{2}\sqrt{(4 - x^{2})}$.
This makes a circle as shown in the graph.
