Question

A circle is drawn on a coordinate plane with the center point at (-4, 6) and a radius of 2. Derive the equation of the circle from the given information. Fill in the missing information in the following equation.(1 point) (x- )2 + (y - )2 =

Answer 1

The equation of a circle in the coordinate plane can be expressed in the standard form:

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

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

From the given information:
- The center of the circle is at \((-4, 6)\), which means \(h = -4\) and \(k = 6\).
- The radius \(r\) is \(2\).

Now, we need to find \(r^2\):
\[
r^2 = 2^2 = 4
\]

Substituting these values into the standard equation gives us:

\[
(x - (-4))^2 + (y - 6)^2 = 4
\]

This simplifies to:

\[
(x + 4)^2 + (y - 6)^2 = 4
\]

Now, filling in the missing information in your equation format:

\[
(x - (-4))^2 + (y - 6)^2 = 4
\]

So the final filled-in equation looks like this:

\[
(x + 4)^2 + (y - 6)^2 = 4
\]