Three Points on a circle: (-17,-2), (0,15), (9,-2). What is the equation of the circle?
+179 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 \(\left(x+4\right)^{2}+\left(y-2\right)^{2}=185\)
