A circle is drawn on a coordinate plane with the center point at (−4,6)

Question

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:

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