Question

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

Answer 1

Circumference is `24pi` and area is `144pi`

Explanation:

As the circle has center at `(0,0)` and passes through `(-12,0)`, its radius is

distance between `(0,0)` and `(-12,0)`

i.e. `sqrt((-12-0)^2+(0-0)^2)=sqrt(144+0)=12`

As radius is `12`,

Circumference is `2xxpixxr=2pixx12=24pi`

and area is `pixx12^2=pixx144=144pi`

Answer 2

`24pi,` `144pi`

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)`

`rarrsqrt((-12-0)^2+(0-0)^2)`

`rarrsqrt(144)`

`color(green)(rArr12`

We know the radius, let's find the circumference

`color(brown)("Circumference"=2pir`

`rarr2*pi*12`

`rarr528/7`

`color(green)(rArr24pi`

Now find the area

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

`rarrpi*12^2`

`color(green)(rArr144pi`

Hope this helps...:)