Pre-Algebra Examples

$5 y^{2} = 25 - 5 x^{2}$

Step 1

Move all terms containing variables to the left side of the equation.

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Step 1.1

Add $5 x^{2}$ to both sides of the equation.

$5 y^{2} + 5 x^{2} = 25$

Step 1.2

Reorder $5 y^{2}$ and $5 x^{2}$ .

$5 x^{2} + 5 y^{2} = 25$

Step 2

Divide both sides of the equation by $5$ .

$x^{2} + y^{2} = 5$

Step 3

This is the form of a circle. Use this form to determine the center and radius of the circle.

${(x - h)}^{2} + {(y - k)}^{2} = r^{2}$

Step 4

Match the values in this circle to those of the standard form. The variable $r$ represents the radius of the circle, $h$ represents the x-offset from the origin, and $k$ represents the y-offset from origin.

$r = \sqrt{5}$

$h = 0$

$k = 0$

Step 5

The center of the circle is found at $(h, k)$ .

Center: $(0, 0)$

Step 6

These values represent the important values for graphing and analyzing a circle.

Center: $(0, 0)$

Radius: $\sqrt{5}$

Step 7