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

Question

Write x2+y2+4x+6y=23 in the standard form of a circle and then identify the circle's center and radius.
Enter the radius exactly. Do not use a decimal approximation.
The radius is.....
Enter the center as an ordered pair, including the comma.
The center is a....

Answer 1

Write x2+y2+4x+6y=23 in the standard form of a circle and then identify the circle's center and radius.
Enter the radius exactly. Do not use a decimal approximation.
The radius is.....
Enter the center as an ordered pair, including the comma.
The center is a....

 

 

x2+y2+4x+6y=23

 

complete the squares for both x and y

x2+4x+4

+y2+6y+9=23+9+4

(x+2)² + (y+3)² =36=6²

 

Standard form is 

(x-a)²+ (y-b)² = r²

 

center of circle is (-2, -3)

 

radius of circle is 6