Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.

Suppose you have a sphere tangent to the $xy$-plane with its center having a positive $z$-coordinate. If it is projected from a point $P=(0,b,a)$ to the $xy$-plane, it gives the conic section $y=x^2$. If we write $a=\frac{p}{q}$ where $p$ and $q$ are integers, find $p+q$.

Remember to put your answer on its own line after "Answer:".
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