The center of a circle is located at (−2, 7) . The radius of the circle is 2.
What is the equation of the circle in general form?
A circle can be defined as the locus of all points that satisfy the equation
(x−h)2+(y−k)2=r2 ( Standard Form )
where r is the radius of the circle,
and h,k are the coordinates of its center.
The general Form is:
x2+y2+ax+by+c=0
Standard Form to general Form:
(x−h)2+(y−k)2=r2x2−2xh+h2+y2−2yk+k2=r2x2+y2+x⋅(−2h)⏟=a+y⋅(−2k)⏟=b+h2+k2−r2⏟=c=0
a,b and c ?
x2+y2+x⋅(−2h)⏟=a+y⋅(−2k)⏟=b+h2+k2−r2⏟=c=0a=−2hb=−2kc=h2+k2−r2
If we have h,k and r, we can calculate a,b and c:
x2+y2+ax+by+c=0a=−2hb=−2kc=h2+k2−r2
h=−2k=7r=2
a=−2ha=−2⋅(−2)a=4b=−2kb=−2(7)a=−14c=h2+k2−r2c=(−2)2+72−22c=4+49−4c=49x2+y2+ax+by+c=0x2+y2+4x−14y+49=0
The equation of the circle in general form is: x2+y2+4x−14y+49=0
