What is the radius of a circle whose equation is x2+y2+8x−6y+21=0?

Radius=2

Center: (-4,3)

Step-by-step explanation:

The general equation of a circle is

(x-xo)²+(y-yo)²=r², where (xo,yo) are the coordinates of the center, and r is the radius.

Now: x²+y²+8x−6y+21=0

x²+8x+y²-6y+21=0

(x²+8x+16-16)+(y²-6y+9-9)+21=0

(x²+8x+16)-16+(y²-6y+9)-9+21=0

(x+4)²+(y-3)²-16-9+21=0

(x+4)²+(y-3)²=16+9-21=25-21=4=2²

So

(x+4)²+(y-3)²=2².

Thus, the radius is 2.

The center is at (-4,3)

256π units²   (answer b)

step-by-step explanation:

the formula for the surface area of a sphere of radius r

is             a = 4πr²

and so, if r = 8 units, then the surface area is:

a = 4π(8 units)² = 256π units²   (answer b)