Question

The equation for a circle is (x+8)2+(y−12)2=25

What is the coordinate of the center of the circle?

What is the radius of the circle?

Answer 1

The general equation for a circle in the Cartesian coordinate system is given by:

\[
(x - h)^2 + (y - k)^2 = r^2
\]

where \((h, k)\) is the center of the circle and \(r\) is the radius of the circle.

Given the equation of the circle:

\[
(x + 8)^2 + (y - 12)^2 = 25
\]

we can rearrange it to match the general form by recognizing that \(+8\) can be written as \(-(-8)\):

\[
(x - (-8))^2 + (y - 12)^2 = 25
\]

From this, we see that the center \((h, k)\) of the circle is \((-8, 12)\).

To find the radius \(r\), we note that the right-hand side of the equation is \(25\). Since \(r^2 = 25\), we take the square root of both sides to get:

\[
r = \sqrt{25} = 5
\]

So, summarizing:
- The coordinate of the center of the circle is \((-8, 12)\).
- The radius of the circle is \(5\).