(a) Find the \( y \)-intercepts of the graph of \( \frac{x^{2}}{4}+\frac{y^{2}}{9}=1 \)

To find the \( y \)-intercepts of the given equation \( \frac{x^{2}}{4}+\frac{y^{2}}{9}=1 \), we set \( x = 0 \) and solve for \( y \). Plugging \( x = 0 \) into the equation gives: \[ \frac{0^{2}}{4} + \frac{y^{2}}{9} = 1 \] This simplifies to: \[ \frac{y^{2}}{9} = 1 \] Multiplying both sides by 9 yields: \[ y^{2} = 9 \] Taking the square root of both sides, we find: \[ y = 3 \quad \text{or} \quad y = -3 \] Thus, the \( y \)-intercepts of the graph are \( (0, 3) \) and \( (0, -3) \).