Precalculus Examples

x^{2} + {(y - 1)}^{2} = 1

$x^{2} + {(y - 1)}^{2} = 1$

Step 1

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 2

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 = 1

$k = 1$

Step 3

The center of the circle is found at

(h, k)

$(h, k)$ .

Center:

(0, 1)

$(0, 1)$

Step 4

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

Center:

(0, 1)

$(0, 1)$

Radius:

1

$1$

Step 5

x^{2} + {(y - 1)}^{2} = 1

$x^{2} + {(y - 1)}^{2} = 1$

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