Question

How do you write the equation of a circle with a center at (7, 3) and a diameter of 24?

Answer 1

`(x-7)^2+(y-3)^2=12^2`

Explanation:

If the diameter is `24` then the radius is `r=24/2=12`

The general formula for a circle with center `(a,b)` and radius `r` is
`color(white)("XXX")(x-a)^2+(y-b)^2=r^2`

Substituting the given values for `(a,b)` and the calculated value for `r` gives
`color(white)("XXX")(x-7)^2+(y-3)^2=12^2`

Personally I think the equation should be left in this form. (it provides the maximum amount of information).

However if you need it "expanded":
`color(white)("XXX")x^2-14x+49+y^2-6y+9=144`

`color(white)("XXX")x^2+y^2-14x-6y=86`