# A circle has center at (0,0) and passes through (-12,0), what is its circumference and area?

Mar 30, 2017

Circumference is $24 \pi$ and area is $144 \pi$

#### Explanation:

As the circle has center at $\left(0 , 0\right)$ and passes through $\left(- 12 , 0\right)$, its radius is

distance between $\left(0 , 0\right)$ and $\left(- 12 , 0\right)$

i.e. $\sqrt{{\left(- 12 - 0\right)}^{2} + {\left(0 - 0\right)}^{2}} = \sqrt{144 + 0} = 12$

As radius is $12$,

Circumference is $2 \times \pi \times r = 2 \pi \times 12 = 24 \pi$

and area is $\pi \times {12}^{2} = \pi \times 144 = 144 \pi$

Mar 30, 2017

$24 \pi ,$ $144 \pi$

#### Explanation:

color(blue)((0,0)and(-12,0)

The distance between these points is the radius of the circle

color(brown)("Distance"=sqrt((x_2-x_1)^2+(y_2-y_1)^2)

$\rightarrow \sqrt{{\left(- 12 - 0\right)}^{2} + {\left(0 - 0\right)}^{2}}$

$\rightarrow \sqrt{144}$

color(green)(rArr12

We know the radius, let's find the circumference

color(brown)("Circumference"=2pir

$\rightarrow 2 \cdot \pi \cdot 12$

$\rightarrow \frac{528}{7}$

color(green)(rArr24pi

Now find the area

color(brown)("Area"=pir^2

$\rightarrow \pi \cdot {12}^{2}$

color(green)(rArr144pi

Hope this helps...:)