Question

The end points of the diameter of a circle are (6, 0) and (-6, 0). What is the equation of this circle?

Answer 1

Equation of a Circle

Circular equations are organized like this:

`(x-h)^2+(y-k)^2=r^2`

• 
  `(h,k)` is the center of the circle
• 
  `r` is the radius

Solving the Question

We're given:

• (6, 0) and (-6, 0) are the endpoints of the diameter of a circle

To find the equation of this circle, we must determine two things:

• The center of the circle
• The radius

To determine the radius of the circle, find the distance between the given endpoints and divide by 2:

(6, 0) and (-6, 0)

⇒ There are 6 units between (0,0) and (6,0).

⇒ There are 6 units between (0,0) and (-6,0).

⇒ 6 + 6 = 12; the diameter of the circle is 12 units

⇒ 12 / 2 = 6

Therefore, the radius of the circle is 6 units.

To determine the center of the circle, find the midpoint of the given endpoints:

(6, 0) and (-6, 0)

⇒ The midpoint occurs at the very middle of these two points. The distance between the midpoint and (6,0) is equal to the distance between the midpoint and (-6,0).

⇒ We identified earlier that there are 6 units between (0,0) and (6,0), and that there are 6 units between (0,0) and (-6,0).

Therefore, the center of the circle is (0,0).

Plug the center and the radius into the equation:

`(x-h)^2+(y-k)^2=r^2\\x^2+y^2=6^2\\x^2+y^2=36`

Answer

`x^2+y^2=36`