Answer to Question #113766 in Analytic Geometry for randal

Question

Find the equation of the circle whose center is at (3, -5) and whose radius is 4

Answer 1

We have center of the circle $(h, k) = (3, -5)$ and

Radius =$r = 4$

We know the equation of the circle with center and radius

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

Now we can plug the center and radius

$$(x - 3)^2 + (y +5)^2 = 4^2$$

$$x^2 +9 -6x +y^2 +25 +10y = 16$$

$$x^2 + y^2 - 6x + 10y + 18 =0$$

Answer: Equation of circle is $x^2 + y^2 - 6x + 10y + 18 =0$