Question

How do you write the equation of the circle with center (2,4) and containing the point (-2,1)?

Answer 1

`25=(x-2)^2+(y-4)^2`

Explanation:

The equation of a circle with center `(h,k)` and radius `r` is:
`r^2=(x-h)^2+(y-k)^2`

We are told that the center of this circle is `(2,4)`, so
`r^2=(x-2)^2+(y-4)^2`

However, we don't know the radius of this circle. Luckily, we are also told that this circle contains the point `(-2,1)`, so we will use that information to find `r`:
`r^2=(x-2)^2+(y-4)^2`
`r^2=(-2-2)^2+(1-4)^2`
`r^2=16+9`
`r^2=25`
`r=5`

The radius of the circle is `5`, which means the equation of the circle is:
`25=(x-2)^2+(y-4)^2`