Question

In standard form, find the equation of the circle that passes through the origin and x-intercept 1 and y-intercept 2.

(I fixed a correction a little too late after a response.)

Help please?

thanks!

Answer 1

so for (x-h)^2 + (y-k)^2 = r^2

for (0,0) ---> h^2 + k^2 = r^2 #(1)
for (1,0) ---> (1-h)^2 + k^2 = r^2 #(2)
for (0,2) ---> h^2 + (2-k)^2 = r^2 #(3)

#2 - #1 :
(1-h)^1 - h^2 = 0
-2h + 1 = 0
h = 1/2

#3-#1 :
(2-k)^ - k^2 = 0
-4k + 4 = 0
k = 1

so (x - 1/2)^2 + (y-1)^2 = r^2
at (0,0)
1/4 + 1 = r^2
r^2 = 5/4

so (x - 1/2)^2 + (y-1)^2 = 5/4