A circle is drawn on a coordinate plane with the center (-7, -2) and a radius of 9. 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 standard form is given by:

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

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

For your circle:

• The center is \((-7, -2)\), which means \(h = -7\) and \(k = -2\).
• The radius is \(9\), so \(r^2 = 9^2 = 81\).

Now, substituting these values into the standard form:

\[ (x - (-7))^2 + (y - (-2))^2 = 81 \]

This simplifies to:

\[ (x + 7)^2 + (y + 2)^2 = 81 \]

So, filling in the missing information, we have:

• \(h = -7\)
• \(k = -2\)
• \(r^2 = 81\)

Thus, the completed equation is:

\[ (x + 7)^2 + (y + 2)^2 = 81 \]