Question

Find the equation for the following circle:

The circle that passes through the origin and has intercepts equal to 1 and 2 on the x- and y-axes, respectively.

Answer 1

That means it must pass though (0,0), (1,0) and (0,2) . The center must be located where the perpendicular bisectors of chords between those points intersect. That would be the point where the vertical line y = 1 and the horizontal ine x= 1/2 intersect, They cross at (1/2, 1) The radius is the distance of that point from any of the three given point, which is
R = sqrt[(1/2)^2 + 1^2] = sqrt (5/4)

Thus the circle equation is
(x-0.5)^2 + (y-1)^2 = 5/4

Check my thinking

Answer 2

y=53