Notes

 

Problems and Videos

For numbers \(1-2\), find the center, the radius and graph the circles

\(\textbf{1)}\) \(x^2+y^2=16\)

Show Center, Radius, and Graph

The answer is center \((0,0) \,\,\), radius \(4\)

 

\(\textbf{2)}\) \((x-3)^2+(y+4)^2=25\)

Show Center, Radius, and Graph

The answer is center \((3,-4) \,\,\), radius \(5\)

 

For numbers \(3-7\), find the equation of the circle

\(\textbf{3)}\) Equation of a circle with endpoints \((4,5)\) and \((-2,-3)\).

Show Equation

The equation is \((x-1)^2+(y-1)^2=25\)

 

\(\textbf{4)}\) Equation of a circle with center \((2,8)\) and tangent to the x axis.

Show Equation

The equation is \((x-2)^2+(y-8)^2=64\)

 

\(\textbf{5)}\) Equation of a circle with center \((-5,3)\) and point on the circle \((7,-2)\).

Show Equation

The equation is \((x+5)^2+(y-3)^2=169\)

 

\(\textbf{6)}\) Equation of a circle with center \((1/2,7)\) and radius \(\sqrt{5}\).

Show Equation

The equation is \((x-\frac{1}{2})^2+(y-7)^2=5\)

 

\(\textbf{7)}\) Write the equation of the circle graphed below.

Show Equation

The equation is \((x+2)^2+(y-4)^2=9\)

 

\(\textbf{8)}\) Use completing the square to find the center and radius of this circle. \(x^2+8x+y^2-6y=11\).

Show Equation, Center and Radius

The equation is \((x+4)^2+(y-3)^2=36,\,\,\)
The center is \((-4,3),\,\,\)
The radius is \(6\)

 

\(\textbf{9)}\) Use completing the square to find the center and radius of this circle. \(x^2+y^2+2x-8y-19=0\).

Show Equation, Center, and Radius

The equation is \((x+1)^2+(y-4)^2=36,\,\,\)
The Center is \((-1,4),\,\,\)
The Radius is \(6\)

 

See Related Pages\(\)

\(\bullet\text{ Circle Graphing Calculator (Desmos.com)}\)
\(\,\,\,\,\,\,\,\,\)

\(\bullet\text{ All Conic Section Notes}\)
\(\,\,\,\,\,\,\,\,\)

\(\bullet\text{ Equation of a Circle}\)
\(\,\,\,\,\,\,\,\,(x-h)^2+(y-k)^2=r^2…\)

\(\bullet\text{ Parabolas}\)
\(\,\,\,\,\,\,\,\,y=a(x-h)^2+k…\)

\(\bullet\text{ Axis of Symmetry}\)
\(\,\,\,\,\,\,\,\,x=-\frac{b}{2a}…\)

\(\bullet\text{ Ellipses}\)
\(\,\,\,\,\,\,\,\,\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1…\)

\(\bullet\text{ Area of Ellipses}\)
\(\,\,\,\,\,\,\,\,\text{Area}=\pi a b…\)

\(\bullet\text{ Hyperbolas}\)
\(\,\,\,\,\,\,\,\,\frac{(x-h)^2}{a^2}-\frac{(y-k)^2}{b^2}=1…\)

\(\bullet\text{ Conic Sections- Completing the Square}\)
\(\,\,\,\,\,\,\,\,x^2+8x+y^2−6y=11 \Rightarrow (x+4)^2+(y−3)^2=36…\)

\(\bullet\text{ Conic Sections- Parametric Equations}\)
\(\,\,\,\,\,\,\,\,x=h+r \cos{t}\)
\(\,\,\,\,\,\,\,\,y=k+r \sin{t}…\)

\(\bullet\text{ Degenerate Conics}\)
\(\,\,\,\,\,\,\,\,x^2−y^2=0…\)

\(\bullet\text{ Andymath Homepage}\)