Question

Equation of a circle

Answer 1

Why would two solutions mean it didn't work?  It's a circle.

Answer 2

It would be unusual to get one solution

Answer 3

Your method is correct. Draw the picture of the circle and see how many points there are where x = 0.

Answer 4

I have vague memories of being confused by this when I was a high-school student, and then the confusion gave way to a kind of wonder as I realized that the multiple roots were exactly right for describing the situation.

Similarly, when you are solving a quadratic to find out when a projectile will hit the ground, you will get two solutions, because the solutions tell you when the projectile is *at* ground level -- and it must have been launched sometime!

Answer 5

Consider the fact that the line x=0 intersects your circle at two points.

Answer 6

For a circle, every x, except for 2 values, yields 2 values of y.