9.12. Circles in the Coordinate Plane http://www.ck12.org
First locate the center. Draw in the horizontal and vertical diameters to see where they intersect.
From this, we see that the center is (-3, 3). If we count the units from the center to the circle on either of these
diameters, we findr=6. Plugging this into the equation of a circle, we get: (x−(− 3 ))^2 + (y− 3 )^2 = 62 or
(x+ 3 )^2 +(y− 3 )^2 =36.
Example C
Determine if the following points are on(x+ 1 )^2 +(y− 5 )^2 =50.
a) (8, -3)
b) (-2, -2)
Plug in the points forxandyin(x+ 1 )^2 +(y− 5 )^2 =50.
a)
( 8 + 1 )^2 +(− 3 − 5 )^2 = 50
92 +(− 8 )^2 = 50
81 + 646 = 50(8, -3) isnoton the circle
b)
(− 2 + 1 )^2 +(− 2 − 5 )^2 = 50
(− 1 )^2 +(− 7 )^2 = 50
1 + 49 = 50