Answer:
center: (0, 0)
radius: 15
Step-by-step explanation:
We are given the equation for a circle:
[tex]2x^2+2y^2=450[/tex]
The standard form of a circle is:
[tex](x-h)^2+(y-k)^2=r^2[/tex]
where:
- [tex](h,k)[/tex] is the center
- [tex]r[/tex] is the radius
We can divide both sides of the given equation by 2 to get it into the standard form:
[tex]\dfrac{2x^2+2y^2}{2}=\dfrac{450}{2}[/tex]
↓↓↓
[tex]x^2 + y^2 = 225[/tex]
Now, we can see that:
[tex]r^2 = 225[/tex]
[tex]r = \sqrt{225}[/tex]
[tex]\boxed{r=15}[/tex]
And, the center is the origin:
(0, 0)
because there are no apparent [tex]h[/tex] and [tex]k[/tex] values. Rather,
[tex]h = k = 0[/tex]
Further Note
We could rewrite the equation with [tex]h[/tex] and [tex]k[/tex], but it would be unnecessarily complicated because subtracting 0 is redundant:
[tex](x-0)^2 + (y-0)^2 = 225[/tex]
