Question

Find the equation of a circle with center (4, 5) and radius 7, and express it in standard form (x - h)^2 + (y - k)^2 = r^2.

Answer 1

To write the equation of a circle in standard form, we use the formula:

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

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

Given the center of the circle as \((4, 5)\) and the radius as \(7\):

1. Identify \(h\), \(k\), and \(r\):
- \(h = 4\)
- \(k = 5\)
- \(r = 7\)

2. Calculate \(r^2\):
\[
r^2 = 7^2 = 49
\]

3. Substitute \(h\), \(k\), and \(r^2\) into the standard form equation:
\[
(x - 4)^2 + (y - 5)^2 = 49
\]

Therefore, the equation of the circle in standard form is:

\[
(x - 4)^2 + (y - 5)^2 = 49
\]