Wize High School Grade 10 Math Textbook > Analytic Geometry

Equation of a Circle around the Centre (Origin)
The formula of a circle on the Cartesian Plane wth centre at the origin O=(0,0)O=\left(0,0\right)O=(0,0) is

x2+y2=r2\Large\boxed{x^2+y^2=r^2}x2+y2=r2​

Wize Tip
Recall the radius (r)\left(r\right)(r) is the distance from the centre of the circle to the edge. It is the same everywhere in the circle!

0:00 / 0:00

Example: Equation of a Circle

a) What is the equation of a circle about the origin O=(0,0)O=\left(0,0\right)O=(0,0) and has a radius of 4?

x2+y2=r2x^2+y^2=r^2x2+y2=r2
x2+y2=42x^2+y^2=4^2x2+y2=42

ANSWER: x2+y2=16x^2+y^2=16x2+y2=16

B) What is the radius of a circle about the origin O=(0,0)O=\left(0,0\right)O=(0,0) and the equation x2+y2=81x^2+y^2=81x2+y2=81

r2=81r2=81r=9\begin{array}{ccc}
r^2&=&81\\
\sqrt{r^2}&=&\sqrt{81}\\
r&=&9
\end{array}r2r2​r​===​8181​9​

ANSWER: The radius is 999

C) What is the radius of a circle about the origin O=(0,0)O=\left(0,0\right)O=(0,0) and  passing through (−4,3)\left(-4,3\right)(−4,3)

x2+y2=r2(−4)2+(3)2=r216+9=r225=r225=r5=r\begin{array}{ccc}
x^2+y^2&=&r^2\\
(-4)^2+(3)^2&=&r^2\\
16+9&=&r^2\\
25&=&r^2\\
\sqrt {25}&=&\sqrt{r}\\
5&=&r

\end{array}x2+y2(−4)2+(3)216+92525​5​======​r2r2r2r2r​r​

ANSWER: The radius is 555

Practice: Equation of a Circle around the Centre (Origin)
a) What is the equation of a circle about the origin O=(0,0)O=\left(0,0\right)O=(0,0) and a radius of 666?

b) What is the radius of a circle about the origin O=(0,0)O=\left(0,0\right)O=(0,0) and the equation x2+y2=23x^2+y^2=23x2+y2=23

c) What is the radius of a circle about the origin O=(0,0)O=\left(0,0\right)O=(0,0) and  passing through (5,−3)\left(5,-3\right)(5,−3)

a) Enter the equation in the form

x^2+y^2=r^2

b) Enter the exact radius (do not round your answer)

c) Enter the exact radius (do not round your answer)

I don't know

Practice: Area of a Circle
A race track is in the shape of a perfect circle. The outer edge of the track has equation x2+y2=49x^2+y^2=49x2+y2=49 and the inner edge of the track has equation x2+y2=9x^2+y^2=9x2+y2=9. Determine the area that this track covers.

Enter the exact area the track covers (do not round your answer), do not include units.

I don't know