Algebra Examples

$1 - y^{2} = x^{2}$

Step 1

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

Tap for more steps...

Step 1.1

Subtract $x^{2}$ from both sides of the equation.

$1 - y^{2} - x^{2} = 0$

Step 1.2

Move $1$ .

$- y^{2} - x^{2} + 1 = 0$

Step 1.3

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

$- x^{2} - y^{2} + 1 = 0$

Step 2

Subtract $1$ from both sides of the equation.

$- x^{2} - y^{2} = - 1$

Step 3

Divide both sides of the equation by $- 1$ .

$x^{2} + y^{2} = 1$

Step 4

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 5

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.

$r = 1$

$h = 0$

$k = 0$

Step 6

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

Center: $(0, 0)$

Step 7

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

Center: $(0, 0)$

Radius: $1$

Step 8