Three Points on a circle: (-17,-2), (0,15), (9,-2). What is the equation of the circle?

Guest Jun 5, 2021

#1**+1 **

The equation for a circle is \((x-a)^2+(y-b)^2=r^2\), where (a, b) is the center, and r is the radius.

Plugging in (x, y) = (-17, -2) into the above equation, we have \((-17-a)^2+(-2-b)^2=r^2\)

Plugging in (x, y) = (0, 15) into the above equation, we have \(a^2+(15-b)^2=r^2\)

Plugging in (x, y) = (9, -2) into the above equation, we have\( (9-a)^2+(-2-b)^2=r^2\).

In this, we have 3 variables (a, b, and r), and 3 equations, and hence can solve for each of them. A bit of algebra later,

a = -4, b = 2, and r = \(\sqrt{185}\).

Substituting these values into the equation for the circle,

The equation becomes \(\left(x+4\right)^{2}+\left(y-2\right)^{2}=185\)

EnchantedLava68 Jun 5, 2021