Q. 59 - Calculus

Question

For each of the equations in Exercises 59–62, y is defined as an implicit function of x. Solve for y, and use what you find to sketch a graph of the equation.

$\frac{1}{4}{x}^2+y^2=9$

Step-by-Step Solution

Answer

The equation for $y$ is $y=\frac{\pm \sqrt{36-x^2}}{2}$

Step 1. Given Information

The given equation is $\frac{1}{4}{x}^2+y^2=9$

Step 2. Finding equation of y

$$\begin{gathered} \frac{1}{4}{x}^2+y^2=9 \\ {y}^2=9-\frac{1}{4}{x}^2=\frac{36-x^2}{4} \\ y=\frac{\pm \sqrt{36-x^2}}{2} \end{gathered}$$

Step 3. Graph of the Equation

We obtained $y=\frac{\pm \sqrt{36-x^2}}{2}$

The graph is of ellipse