Calculus Examples

{(x - 2)}^{2} + y^{2} - 25 = 0

${(x - 2)}^{2} + y^{2} - 25 = 0$

Step 1

Add

25

$25$ to both sides of the equation.

{(x - 2)}^{2} + y^{2} = 25

${(x - 2)}^{2} + y^{2} = 25$

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}

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

Step 3

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

r

$r$ 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 = 5

$r = 5$

h = 2

$h = 2$

k = 0

$k = 0$

Step 4

The center of the circle is found at

(h, k)

$(h, k)$ .

Center:

(2, 0)

$(2, 0)$

Step 5

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

Center:

(2, 0)

$(2, 0)$

Radius:

5

$5$

Step 6