(x+2)2+(y−1)2=10
Step-by-step explanation:
The simplest equation for a circle is:
XXX2+Y2=R2
for a circle with center at (0,0) R
and radius
If we want to shift this so the center is at
(−2,1)
then the
X
values become x=X−2xx→xxX=x+2
and the Y values become yy=Y−1xx → xxY=y−1=Y−1xx→xxY=y−1 So X 2+Y becomes
(x+2)2+(y−1)2
The radius is unaffected by the shift and will remain the same length.
The radius is the distance between the center
(−2,1)
and any point on the circumference; in this case we are given the point
(1,0)
Using the Pythagorean Theorem this gives us a radius squared of
XXXR2=((−2)−1)2+(1−0)2=10
Therefore the equation of our (shifted) circle will be
XXX(x+2)2+(y−1)2=10