Question

How do you write an equation for a circle with center (2,0) and radius sqrt11?

Answer 1

`x^2-4x+y^2-7=0`

Explanation:

The equation of a circle is

`x^2+y^2=r^2`,

where `r` is the radius, given as `sqrt11`, so

`x^2+y^2=sqrt11^2=11`.

You want to get the circle centered around the origin `(0,0)`, which you do by adding or subtracting a certain amount to the `x` and `y` values of the center to get it to `0`.

`x` is given as `2` (the point is `(2,0)`), so you subtract `2`. `y` is `0` so you can leave it the same. This gives an equation of

`(x-2)^2+y^2=11`.

Expanding this out,

`x^2-4x+4+y^2=11`

Rearranging for the final answer,

`x^2-4x+y^2-7=0`