Question

In the following exercises, ⓐ find the center and radius, then ⓑ graph each circle.

$2x^2+2y^2=8$

Short answer

(a) Center of the circle $2x^2+2y^2=8$is $(0,0)$and radius is$2$

(b) graph of the circle is

Step-by-step solution

Step 1. Given data

The given equation of the circle is

$2x^2+2y^2=8$

Step 2. Part (a)

Compare the equation of the circle with the standard equation of the circle

$$\begin{gathered} 2x^2+2y^2=8 \\ 2(x^2+y^2)=2\left(4\right) \\ {x}^2+y^2=4 \\ {(x-0)}^2+{(y-0)}^2=2^2 \\ {(x-h)}^2+{(y-k)}^2=r^2 \end{gathered}$$

so center$(h,k)=(0,0)$

and radius$r=2$

Step 3. Part (b)

Plot the circle of center $(0,0)$and radius$2$