Andrew K. answered • 09/23/19
Expert Math and Physics Tutor - Many successful students!
Hi Carson,
The general equation of a circle is:
(x-x0)2 + (y - y0)2 = r2
where (x0,y0) is the center of the circle, and r is the radius of the circle
So, the only things we need to figure out are the coordinates of the center, and the radius. We already know that the center of the circle is (3,4) so that gives us our x0 and y0. To determine the radius, since we know that the circle is centered at (3,4), and the outside of the circle passes through (-5,1), we can use the pythagorean theorem to calculate the distance between those two points:
a2 + b2 = c2
or
(horizontal distance)2 + (vertical distance)2 = (radius)2
(-5 - 3)2 + (1 - 4)2 = r2
(-8)2 + (-3)2 = r2
64 + 9 = r2
73 = r2
Now, since we know the center and radius2, we can fill in the circle equation:
(x - 3)2 + (y - 4)2 = 73
I hope this helps!
Andy
