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 standard equation of a circle with center \((h, k)\) and radius \(r\) is given by:

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

Given the center point \((-4, 6)\), we have \(h = -4\) and \(k = 6\). The radius is given as \(r = 2\). Therefore, \(r^2 = 2^2 = 4\).

Substituting the values into the equation, 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 provided format:

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

So the answer is:

- **Missing values:**
- \( -4 \)
- \( 6 \)
- \( 4 \)

Thus, the correctly filled equation looks like:

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