Question

How do you find the equation of a circle in standard form given C(1,3) and r=3?

Answer 1

Please see the explanation.

Explanation:

The standard Cartesian form for the equation of a circle is:

`(x - h)^2 + (y - k)^2 = r^2" [1]"`

where x and y are any point, `(x,y)`, on the circle, h and k are the center point, `(h,k)` and r is the radius.

We are given that the center point is, `C(1,3)`, and the radius is 3, therefore, we substitute, 1 for h, 3 for k and 3 for r into equation [1], to obtain the following equation:

`(x - 1)^2 + (y - 3)^2 = 3^2" [2]"`

Equation [2] is the answer.