One way to find the radius of the circle is to put the given equation in standard form,
(x−h)2+(y−k)2=r2,where
(h,k) is the center of the circle and the radius of the circle is r. To do this, divide the original equation,
2x2−6x+2y2+2y=45, by 2 to make the leading coefficients of
x2 and
y2 each equal to
1:x2−3x+y2+y=22.5. Then complete the square to put the equation in standard form. To do so, first rewrite
x2−3x+y2+y=22.5 as
(x2−3x+2.25)−2.25+(y2+y+0.25)−0.25=22.5
.Second, add
2.25 and
0.25 to both sides of the equation:
(x2−3x+2.25)+(y2+y+0.25)=25. Since
x2−3x+2.25=(x−1.5)2,y2−x+0.25=(y−05)2
and
25=52,it follows that
(x−1.5)2+(y−0.5)2=52Therefore, the radius of the circle is 5.
Choices B, C, and D are incorrect and may be the result of errors in manipulating the equation or of a misconception about the standard form of the equation of a circle in the xy-plane.