Determine the graph of the circles given by the following equations.
\left(x-2\right)^2+\left(y-1\right)^2=4
The standard form of a circle is:
\left(x-h\right)^2 + \left(y-k\right)^2 = r^2
The center of the circle is the point \left(h,k\right) and the radius is r.
Here, the equation is:
\left(x-2\right)^2+\left(y-1\right)^2=4
Therefore:
- h=2
- k=1
- r=2
This is the equation of a circle whose center is \left(2{,}1\right) and radius is 2. We can graph this circle as follows:
\left(x-3\right)^2+\left(y+1\right)^2=4
The standard form of a circle is:
\left(x-h\right)^2 + \left(y-k\right)^2 = r^2
The center of the circle is the point \left(h,k\right) and the radius is r.
Here, the equation is:
\left(x-3\right)^2+\left(y+1\right)^2=4
Therefore:
- h=3
- k=-1
- r=2
This is the equation of a circle whose center is \left(3,-1\right) and radius is 2. We can graph this circle as follows:
\left(x+1\right)^2+\left(y-1\right)^2=9
The standard form of a circle is:
\left(x-h\right)^2 + \left(y-k\right)^2 = r^2
The center of the circle is the point \left(h,k\right) and the radius is r.
Here, the equation is:
\left(x+1\right)^2+\left(y-1\right)^2=9
Therefore:
- h=-1
- k=+1
- r=3
This is the equation of a circle whose center is \left(-1{,}1\right) and radius is 3. We can graph this circle as follows:
\left(x+3\right)^2+\left(y-2\right)^2=4
The standard form of a circle is:
\left(x-h\right)^2 + \left(y-k\right)^2 = r^2
The center of the circle is the point \left(h,k\right) and the radius is r.
Here, the equation is:
\left(x+3\right)^2+\left(y-2\right)^2=4
Therefore:
- h=-3
- k=2
- r=2
This is the equation of a circle whose center is \left(-3{,}2\right) and radius is 2. We can graph this circle as follows:
\left(x+1\right)^2+\left(y-1\right)^2=\dfrac{1}{4}
The standard form of a circle is:
\left(x-h\right)^2 + \left(y-k\right)^2 = r^2
The center of the circle is the point \left(h,k\right) and the radius is r.
Here, the equation is:
\left(x+1\right)^2+\left(y-1\right)^2=\dfrac{1}{4}
Therefore:
- h=-1
- k=+1
- r=\dfrac{1}{2}
This is the equation of a circle whose center is \left(-1{,}1\right) and radius is \dfrac{1}{2}. We can graph this circle as follows:
\left(x-2\right)^2+\left(y-2\right)^2=9
The standard form of a circle is:
\left(x-h\right)^2 + \left(y-k\right)^2 = r^2
The center of the circle is the point \left(h,k\right) and the radius is r.
Here, the equation is:
\left(x-2\right)^2+\left(y-2\right)^2=9
Therefore:
- h=-2
- k=-2
- r=3
This is the equation of a circle whose center is \left(2{,}2\right) and radius is 3. We can graph this circle as follows:
\left(x-\dfrac{1}{2}\right)^2+\left(y-1\right)^2=1
The standard form of a circle is:
\left(x-h\right)^2 + \left(y-k\right)^2 = r^2
The center of the circle is the point \left(h,k\right) and the radius is r.
Here, the equation is:
\left(x-\dfrac{1}{2}\right)^2+\left(y-1\right)^2=1
Therefore:
- h=\dfrac{1}{2}
- k=1
- r=1
This is the equation of a circle whose center is \left(\dfrac{1}{2},1\right) and radius is 1. We can graph this circle as follows:
