Write x2+y2+4x+6y=23 in the standard form of a circle and then identify the circle's center and radius.

Question

Write x^2+y^2+4x+6y=23 in the standard form of a circle and then identify the circle's center and radius.
(a)
The standard form of the circle is


a.(x+3)^2−(y+3)^2=6

b.(x+2)^2+(y+3)^2=6

c.(x+2)^2+(y+3)^2=23

d.(x+3)^2+(y+2)^2=23

e.(x+3)^2+(y+2)^2=36

f.(x+2)^2+(y+3)^2=36

 

 

Enter the center as an ordered pair, including the comma.
The center is at .....

Enter the radius exactly. Do not use a decimal approximation.
The radius is.....

Answer 1

Complete the square for the x terms and for the y terms to put the equation in the form (x-h)² + (y-k)² = r².  The center is (h,k) and the radius is r.

 

(x²+4x) + (y²+6y) = 23

 

(x²+4x+4) + (y²+6y+9) = 23+4+9

 

(x+2)² + (y+3)² = 36

 

[x - (-2)]² + [y - (-3)]² = 6²

 

Center:  (-2,-3)     Radius:  6