A circle is drawn on a coordinate plane with the center (3, -5) and a radius of 4. Fill in the missing information to find the equation of the circle.(3 points)

Question

(x−
)2 + (y−
)2 =

Answer 1

The equation of a circle in the coordinate plane can be represented by 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:

• Center \((h, k) = (3, -5)\)
• Radius \(r = 4\)

We first calculate \(r^2\):

\[ r^2 = 4^2 = 16 \]

Now we can fill in the missing parts of the equation of the circle:

\[ (x - 3)^2 + (y + 5)^2 = 16 \]

So, the completed equation is:

\[ (x - 3)^2 + (y + 5)^2 = 16 \]

Thus, the filled form is:

• (x−3)² + (y+5)² = 16