Pre-Algebra Examples

$9 {(x + 2)}^{2} + 9 {(y + 4)}^{2} - 10 = 431$

Step 1

Move all terms not containing a variable to the right side of the equation.

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Step 1.1

Add $10$ to both sides of the equation.

$9 {(x + 2)}^{2} + 9 {(y + 4)}^{2} = 431 + 10$

Step 1.2

Add $431$ and $10$ .

$9 {(x + 2)}^{2} + 9 {(y + 4)}^{2} = 441$

Step 2

Divide both sides of the equation by $9$ .

${(x + 2)}^{2} + {(y + 4)}^{2} = 49$

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.

$r = 7$

$h = - 2$

$k = - 4$

Step 5

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

Center: $(- 2, - 4)$

Step 6

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

Center: $(- 2, - 4)$

Radius: $7$

Step 7