Question

Right triangle ABC is located at A (-1,-2), B(-1, 1), and C (3, 1) on a coordinate plane. What is the equation of a circle A with radius AC?

Olx + 1)2 + y + 2)2 = 9
O(x + 1)2 + (y + 2)2 = 25
OOX - 3)2 + y - 12 = 16
Ox - 3)2 + (y - 142 = 25

Answer 1

(x + 1)2 + (y + 2)2 = 25

Explanation:

Hope this helps :)

Answer 2

(x +1)^2 + (y +2)^2 = 25

Explanation:

A diagram of the given triangle shows you it has side lengths of 3 and 4, so the square of the hypotenuse is ...

(AC)^2 = (AB)^2 +(BC)^2 = 3^2 +4^2

(AC)^2 = 25

The center of the circle is at A(-1, -2), so the equation is ...

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

for the circle centered at (h, k) with radius r.

We know that the square of the radius (r^2) is 25, so we can write the equation as ...

(x +1)^2 +(y +2)^2 = 25