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For numbers \(1-2\), find the center, the radius and graph the circles
\(\textbf{1)}\) \(x^2+y^2=16\) 
\(\textbf{2)}\) \((x-3)^2+(y+4)^2=25\)
For numbers \(3-7\), find the equation of the circle
\(\textbf{3)}\) Equation of a circle with endpoints \((4,5)\) and \((-2,-3)\).
\(\textbf{4)}\) Equation of a circle with center \((2,8)\) and tangent to the x axis.
\(\textbf{5)}\) Equation of a circle with center \((-5,3)\) and point on the circle \((7,-2)\).
\(\textbf{6)}\) Equation of a circle with center \((1/2,7)\) and radius \(\sqrt{5}\).
\(\textbf{7)}\) Write the equation of the circle graphed below.
\(\textbf{8)}\) Use completing the square to find the center and radius of this circle. \(x^2+8x+y^2-6y=11\).
\(\textbf{9)}\) Use completing the square to find the center and radius of this circle. \(x^2+y^2+2x-8y-19=0\).
See Related Pages\(\)
\(\bullet\text{ Circle Graphing Calculator (Desmos.com)}\)
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\(\bullet\text{ All Conic Section Notes}\)
\(\,\,\,\,\,\,\,\,\)
\(\bullet\text{ Equation of a Circle}\)
\(\,\,\,\,\,\,\,\,(x-h)^2+(y-k)^2=r^2…\)
\(\bullet\text{ Parabolas}\)
\(\,\,\,\,\,\,\,\,y=a(x-h)^2+k…\)
\(\bullet\text{ Axis of Symmetry}\)
\(\,\,\,\,\,\,\,\,x=-\frac{b}{2a}…\)
\(\bullet\text{ Ellipses}\)
\(\,\,\,\,\,\,\,\,\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1…\)
\(\bullet\text{ Area of Ellipses}\)
\(\,\,\,\,\,\,\,\,\text{Area}=\pi a b…\)
\(\bullet\text{ Hyperbolas}\)
\(\,\,\,\,\,\,\,\,\frac{(x-h)^2}{a^2}-\frac{(y-k)^2}{b^2}=1…\)
\(\bullet\text{ Conic Sections- Completing the Square}\)
\(\,\,\,\,\,\,\,\,x^2+8x+y^2−6y=11 \Rightarrow (x+4)^2+(y−3)^2=36…\)
\(\bullet\text{ Conic Sections- Parametric Equations}\)
\(\,\,\,\,\,\,\,\,x=h+r \cos{t}\)
\(\,\,\,\,\,\,\,\,y=k+r \sin{t}…\)
\(\bullet\text{ Degenerate Conics}\)
\(\,\,\,\,\,\,\,\,x^2−y^2=0…\)
\(\bullet\text{ Andymath Homepage}\)
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