Pre-Algebra Examples

$34 = {(x - 4)}^{2} + {(y + 7)}^{2}$

Step 1

Since $y$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

${(x - 4)}^{2} + {(y + 7)}^{2} = 34$

Step 2

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 3

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.

$r = \sqrt{34}$

$h = 4$

$k = - 7$

Step 4

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

Center: $(4, - 7)$

Step 5

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

Center: $(4, - 7)$

Radius: $\sqrt{34}$

Step 6