Algebra Examples

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

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

Step 1

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

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Step 1.1

Subtract

x^{2}

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

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

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

Step 1.2

Move

1

$1$ .

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

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

Step 1.3

Reorder

- y^{2}

$- y^{2}$ and

- x^{2}

$- x^{2}$ .

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

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

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

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

Step 2

Subtract

1

$1$ from both sides of the equation.

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

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

Step 3

Divide both sides of the equation by

- 1

$- 1$ .

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

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

Step 5

Match the values in this circle to those of the standard form. The variable

r

$r$ represents the radius of the circle,

h

$h$ represents the x-offset from the origin, and

k

$k$ represents the y-offset from origin.

r = 1

$r = 1$

h = 0

$h = 0$

k = 0

$k = 0$

Step 6

The center of the circle is found at

(h, k)

$(h, k)$ .

Center:

(0, 0)

$(0, 0)$

Step 7

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

Center:

(0, 0)

$(0, 0)$

Radius:

1

$1$

Step 8