Question

Give the equation of the circle whose center is (5 -3) and goes through (2 5)

Answer 1

Explanation:

The standard form for the equation of a circle is

`(x-h)^2+(y-k)^2=r^2`

From the info given, we have the center, (h, k) as (5, -3) and the x and y coordinates of (2, 5). We will use these to solve for r-squared, then plug back in what we need to write the equation.

`(2-5)^2+(5-(-3))^2=r^2` which simplifies to

`(-3)^2+(8)^2=r^2` and

`9+64=r^2` so

`r^2=73`

Filling in the equation:

`(x-5)^2+(y+3)^2=73`