In the rectangular coordinate system, points (4, 0) and (– 4, 0) both lie on circle C. What is the
maximum possible value of the radius of C ?
E. There is no finite maximum value.
I know the OA.. So please dont post A,B..type answers.Please explain your work.
Here is how I would've solved on the actual exam. Since you know that the center lies anywhere on y-axis -> E is the answer
Trying to come up with explanation. One - geometrically - draw a triangle AOB, AO = BO, etc
Analytically: (a,b) center of the circle. (x-a)^2 + (y-b)^2 = R^2
(4-a)^2 + (0-b)^2 = R^2
(-4-a)^2 + (0-b)^ = R^2
subtract those two. 16*a = 0 -> a = 0
put it back: R^2 = 16 + b^2
Easy to see that for any b, there is a circle x^2 + (y-b)^2 = b^2+16 that goes through both (-4,0) and (4,0) -> E