Question

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

Answer 1

Answer:

Step-by-step 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:

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