Determine the center and radius of the following circle equation: x 2 + y 2 − 1 8 x − 6 y + 9 = 0 x 2 +y 2 −18x−6y+9=0?

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Answer 1 · 2018-05-18T02:19:00

#radius=9#
#C:(9,3)#

#x^2 + y^2 − 1 8 x − 6 y + 9 = 0 #

Start by moving the #9# over to the other side:
#x^2 + y^2 − 1 8 x − 6 y = -9 #

Now complete the square using #(b/a)^2#:
#x^2 -18x+81+ y^2 − 6 y+9 = -9 +90#

#(x-9)^2+(y-3)^2= 81#

Since the circle equation is written in the form:
#(x-h)^2+(y-k)^2= r^2#

#r# is the radius
and #(h,k)# is the center

#radius=9#
#C:(9,3)#

Determine the center and radius of the following circle equation: x 2 + y 2 − 1 8 x − 6 y + 9 = 0 x ​2 ​​ +y ​2 ​​ −18x−6y+9=0?