Use completing the square to identify the coordinates of the circle's center

Question

5. The general equation of a circle is x^2 + y^2 - 12y +20 = 0

a. Use completing the square to identify the coordinates of the circle's center

AND the length of the circle's radius.

b. Is the point ( 17, 7) located on this circle? Explain your reasoning.

Answer 1

x² + (y² - 12y) = -20

x² + (y² - 12y + 36) = -20 + 36

(x - 0)² + (y - 6)² = 16

Center = (0,6) and radius = √16 = 4

The point (17,7) is not on the circle since substituting 17 for x and 7 for y into the equation of the circle yields a false statement.

Answer 2

General equation for a circle is

(x-h)^2 + (y-k)^2 = r^2

h=0 for the given equation

now find k

(h,k) is the center of the circle

by completing the square

y^2 -12y +20

= y^2 -12y + 36 +20 -36

just take half of 12 = 6 and square it, then add and subtract 36

=(y-6)^2 -16

k=6

r=square root of 16 =4

the equation is

x^2 + (y-6)^2 = 16

center is (0,6), radius = 4

check the point (17,7)

17^2 + (7-6)^2 = 16

289 +1 =16

290 =16 doesn't work

the point is not on the circle

Someone might have thought so though if they missed the squared sign on the 17

otherwise 17-1 would equal 16