QuestionFind the center of the circle from the equation $225x^{2}+225y^{2}=225$ . Simplify if needed.

Studdy Solution

STEP 1

Assumptions1. The given equation represents a circle in the standard form. . The standard form of a circle's equation is $(x-h)^{}+(y-k)^{}=r^{}$ , where $(h, k)$ is the center of the circle and $r$ is the radius.

STEP 2

The given equation is $225x^{2}+225y^{2}=225$ . To simplify the equation, we can divide every term by225.
$\frac{225x^{2}}{225}+\frac{225y^{2}}{225}=\frac{225}{225}$

STEP 3

implify the equation.
$x^{2}+y^{2}=1$

STEP 4

Now that we have the equation in standard form, we can identify the center of the circle. The center of the circle is given by the coordinates $(h, k)$ in the standard form of the equation.
In this case, since there are no $x$ or $y$ terms, we can conclude that the center of the circle is at the origin, $(0,0)$ .
The center of the circle given by the equation $225x^{2}+225y^{2}=225$ is $(0,0)$ .

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