Question

A circle is defined by the equation given below.

x²+y²-8x-6y+2 =0
What are the coordinates for the center of the circle and the length of the radius?

Answer 1

(1/2, 1) 2 units

Explanation:

center (1/2, 1) radius 2 units

Answer 2

The circle equation is in the format (x – h)2 + (y – k)2= r2, with the center being at the point (h, k) and the radius being "r".

x²+y²-8x-6y+2 =0 -----(a)
(x-4)² = x² - 8x + 16
(y-3)² = y² - 6y + 9

Equation (a) can be rewritten as:
(x-4)² + (y-3)² + 2 - 16 - 9 = 0
(x-4)² + (y-3)² = 23

The coordinates for the center of the circle is: ( 4,3)
The radius is √23=4.8