Graphing circles

Just as there’s an equation for a straight line, there’s also an equation for a circle. The circle equation is a little more involved than $y=mx+b$, but it follows a clear idea: every point on the circle is the same distance from the center.

A circle can be described by

$(x-a{)}^2+(y-b{)}^2=r^2$

where:

• $a$ and $b$ are the $x$- and $y$-coordinates of the center, $(a,b)$
• $r$ is the radius
• $(x,y)$ represents any point on the circle

Please note: you don’t substitute the center coordinates for $x$ and $y$. The variables $x$ and $y$ represent the infinitely many points on the circle. The center coordinates replace only $a$ and $b$.

If the center of the circle is at the origin, $(0,0)$, the equation simplifies because $a=0$ and $b=0$. For example, a circle centered at the origin with radius $2$ has equation $x^2+y^2=2$. Try using the circle equation to solve the problem below.

$(x-a{)}^2+(y-b{)}^2=r^2$

Which of the following equations represents the circle drawn below? The two points represent the highest and lowest points of the circle.

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Answers:
A. $(x+5{)}^2+(y-4{)}^2=36$
B. $(x+5{)}^2+(y-4{)}^2=3$
C. $(x-5{)}^2+(y+4{)}^2=9$
D. $(x+5{)}^2+(y-4{)}^2=9$
E. $(x-5{)}^2+(y+4{)}^2=36$