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

Question

Allison Allen · Accepted Answer

Circumference is #24pi# and area is #144pi# 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#

Jayden Jackson · Answer

#24pi,# #144pi#

#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...:)

Evelyn Arboleda · Answer

undefined To find the circumference of a circle, you can use the formula: $ C = 2\pi r $, where $ r $ is the radius of the circle.

Given that the center of the circle is at (0,0) and it passes through (-12,0), the distance from the center to any point on the circle is the radius.

Using the distance formula, $ r = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $, where $ (x_1, y_1) $ is the center (0,0) and $ (x_2, y_2) $ is a point on the circle (-12,0).

$ r = \sqrt{(-12 - 0)^2 + (0 - 0)^2} = \sqrt{(-12)^2 + 0^2} = \sqrt{144} = 12 $

Now, substitute the radius into the formula for the circumference:

$ C = 2\pi \times 12 = 24\pi $ units.

To find the area of the circle, you can use the formula: $ A = \pi r^2 $.

Substitute the radius into the formula:

$ A = \pi \times 12^2 = \pi \times 144 = 144\pi $ square units.