Center at (2,m), radius is twice the y-coordinate of the center, and passes through the point (0,1) Find the missing y- coordinate and the radius.
Graph the circle
+129842 The equation of the circle is
(x - 2)^2 + (y - m)^2 = (2m)^2 and we know that, since the circle passes through (0, 1), we have
(0 - 2)^2 + (1 - m)^2 = (2m)^2 simplify and solve for m
4 + m^2 - 2m + 1 = 4m^2
3m^2 + 2m - 5 = 0 factor
(3m + 5) (m -1) = 0 setting each factor to 0, we have two possible centers
3m + 5 = 0 → m = -5/3
m - 1 = 0 → m = 1
So ....one possible circle is centered at (2, -5/3) and has a radius of 2(-5/3) = -10/3
But the radius cannot have a negative value, so let's reject this answer
The other answer is that the circle is centered at ( 2,1) and has a radius of 2(1) = 2
Here's the graph : https://www.desmos.com/calculator/yd17fcqnjv
