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.(2 points)
(x−
)2+
(y−
)2=

Answer 1

To derive the equation of a circle from its center and radius, we use the standard form of the equation of a circle, which is:

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

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

From the information given:
- The center \((h, k)\) is \((-4, 6)\), so \(h = -4\) and \(k = 6\).
- The radius \(r\) is \(2\), so \(r^2 = 2^2 = 4\).

Substituting these values into the standard form, we get:

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

This simplifies to:

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

Now filling in the missing information in the equation format provided:

The completed equation is:

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

So, the missing values are:
- The first blank: -4
- The second blank: 6
- The third blank: 4

Thus, the final answer is:

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

or simply:

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