The general form of the equation of a circle is x2 + y2 + 8x + 22y + 37 = 0.
the equation of this circle in standard form is (x +
)2 + (y +
)2 =
. the center of the circle is at the point (
,
).

we know that

the equation of the circle in standard form is equal to

where

is the center of the circle

r is the radius of the circle

we have

Convert to standard form

Group terms that contain the same variable, and move the constant to the opposite side of the equation

Complete the square twice. Remember to balance the equation by adding the same constants to each side

Rewrite as perfect squares

the  center is the point

the radius is

therefore

The answer is

a) the equation in standard form is

b) the  center of the circle is the point and the radius of the circle is

see the attached figure to better understand the problem

answer: the correct answer is -32

step-by-step explanation: