In the general form 2x2+2y2+4x−8y−22=0, how do you convert to standard form?
1 Answer
Feb 6, 2016
(x+1)2+(y−2)2=16
Explanation:
the general equation of a circle is:
x2+y2+2gx+2fy+c=0 To get the equation given here into this form , require to divide through by 2.
( dividing by 2 ) :
x2+y2+2x−4y−11=0 Comparing this equation to the general one we can extract
2g = 2 → g = 1 , 2f = -4 → f = -2 and c = - 11
from this we obtain : centre = (-g , -f ) = (-1 , 2 )
and radius
r=√g2+f2−c=√12+(−2)2+11=4 equation of a circle in standard form is :
(x−a)2+(y−b)2=r2
where (a , b ) are the coords of centre and r is the radiusstandard form :
(x+1)2+(y−2)2=16
