How do you convert the general form of the equation of a circle 2x2+2y2+4y=0 to standard form?
1 Answer
Jan 18, 2016
x2+(y+1)2=1
Explanation:
The standard form is :
(x−a)2+(y−b)2=r2 where (a , b ) are the coordinates of centre and r is radius . These have to be found by rearranging the general form .
general form is :
x2+y2+2gx+2fy+c=0 the one here :
2x2+2y2+4y=0 (divide both sides by 2 ) :
x2+y2+2y=0 ( comparing this to the general form ) : g = 0 , 2f = 2 so f = 1
and c = 0 .centre = ( - g , - f ) = ( 0 ,- 1 ) and
r=√g2+f2−c=√0+12−0=√1=1 equation in standard form is ;
(x−0)2+(y+1)2=12
⇒x2+(y+1)2=1
