Question

match the graphs to their equations.

\frac{(x+2)^2}{9} + \frac{(y+2)^2}{1} = 1

\frac{(x-2)^2}{1} + \frac{(y+2)^2}{9} = 1

\frac{(x+2)^2}{1} + \frac{(y-2)^2}{9} = 1

\frac{(x-2)^2}{9} + \frac{(y-2)^2}{1} = 1

Explanation:

Step1: Identify standard ellipse form

$$\frac{(x-h)^2}{a^2} + \frac{(y-k)^2}{b^2} = 1$$

Step2: Find center of first equation

$$(h, k) = (-2, -2)$$

Step3: Match first equation to graph

$$\text{Center } (-2, -2) \text{ matches graph a.}$$

Step4: Find center of fourth equation

$$(h, k) = (2, 2)$$

Step5: Match fourth equation to graph

$$\text{Center } (2, 2) \text{ matches graph b.}$$

Step6: Find center of second equation

$$(h, k) = (2, -2)$$

Step7: Match second equation to graph

$$\text{Center } (2, -2) \text{ matches graph d.}$$

Step8: Find center of third equation

$$(h, k) = (-2, 2)$$

Step9: Match third equation to graph

$$\text{Center } (-2, 2) \text{ matches graph c.}$$

Answer:

• First equation: \(\frac{(x+2)^2}{9} + \frac{(y+2)^2}{1} = 1\) matches with graph a.
• Second equation: \(\frac{(x-2)^2}{1} + \frac{(y+2)^2}{9} = 1\) matches with graph d.
• Third equation: \(\frac{(x+2)^2}{1} + \frac{(y-2)^2}{9} = 1\) matches with graph c.
• Fourth equation: \(\frac{(x-2)^2}{9} + \frac{(y-2)^2}{1} = 1\) matches with graph b.