Find the equation of the following circles.
The equation of a circle is:
\left(x-h\right)^2+\left(y-k\right)^2=r^2
Where \left(h,k\right) is the center of the circle and r is the radius.
Here:
- The center is \left(h,k\right) = \left(2{,}1\right)
- The radius is the distance between the center and any point of the circle. \left(0{,}1\right) is on the circle, therefore the radius is r=2.
The equation is:
\left(x-2\right)^2+\left(y-1\right)^2=4
The equation of a circle is:
\left(x-h\right)^2+\left(y-k\right)^2=r^2
Where \left(h,k\right) is the center of the circle and r is the radius.
Here:
- The center is \left(h,k\right) = \left(-1{,}2\right)
- The radius is the distance between the center and any point of the circle. \left(1{,}2\right) is on the circle, therefore the radius is r=2.
The equation is:
\left(x+1\right)^2+\left(y-2\right)^2=4
The equation of a circle is:
\left(x-h\right)^2+\left(y-k\right)^2=r^2
Where \left(h,k\right) is the center of the circle and r is the radius.
Here:
- The center is \left(h,k\right) = \left(-2{,}0\right)
- The radius is the distance between the center and any point of the circle. \left(-1{,}0\right) is on the circle, therefore the radius is r=1.
The equation is:
\left(x+2\right)^2+y^2=1
The equation of a circle is:
\left(x-h\right)^2+\left(y-k\right)^2=r^2
Where \left(h,k\right) is the center of the circle and r is the radius.
Here:
- The center is \left(h,k\right) = \left(-2{,}1\right)
- The radius is the distance between the center and any point of the circle. \left(-2{,}3\right) is on the circle, therefore the radius is r=2.
The equation is:
\left(x+2\right)^2+\left(y-1\right)^2=4
The equation of a circle is:
\left(x-h\right)^2+\left(y-k\right)^2=r^2
Where \left(h,k\right) is the center of the circle and r is the radius.
Here:
- The center is \left(h,k\right) = \left(-1{,}1\right)
- The radius is the distance between the center and any point of the circle. \left(-\dfrac{1}{2},1\right) is on the circle, therefore the radius is r=\dfrac{1}{2}.
The equation is:
\left(x+1\right)^2+\left(y-1\right)^2=\dfrac{1}{4}
The equation of a circle is:
\left(x-h\right)^2+\left(y-k\right)^2=r^2
Where \left(h,k\right) is the center of the circle and r is the radius.
Here:
- The center is \left(h,k\right) = \left(3{,}0\right)
- The radius is the distance between the center and any point of the circle. \left(0{,}0\right) is on the circle, therefore the radius is r=3.
The equation is:
\left(x-3\right)^2+y^2=9
The equation of a circle is:
\left(x-h\right)^2+\left(y-k\right)^2=r^2
Where \left(h,k\right) is the center of the circle and r is the radius.
Here:
- The center is \left(h,k\right) = \left(-4{,}1\right)
- The radius is the distance between the center and any point of the circle. \left(-4,-1\right) is on the circle, therefore the radius is r=2.
The equation is:
\left(x+4\right)^2+\left(y-1\right)^2=4