Question

How do you write an equation for a circle given center (0,3) and radius is 7 units?

Answer 1

`x^2 + (y-3)^2 = 7^2`, or
`x^2 + y^2-6y-40 =0`

Explanation:

The Cartesian equation of a circle with centre `(a,b)` and radius `r` is:

`(x-a)^2 + (y-b)^2 = r^2`

So a circle with centre `(0,3)` and radius `7` would be:

`(x-0)^2 + (y-3)^2 = 7^2`
`:. \ \ \ \ \x^2 + (y-3)^2 = 7^2`

We can multiply out if required to get:

`\ \ \ \ \ \ \x^2 + y^2-6y+9 = 49`
`:. x^2 + y^2-6y-40 =0`