Solve the following math problem efficiently and clearly:

- For simple problems (2 steps or fewer):
Provide a concise solution with minimal explanation.

- For complex problems (3 steps or more):
Use this step-by-step format:

## Step 1: [Concise description]
[Brief explanation and calculations]

## Step 2: [Concise description]
[Brief explanation and calculations]

...

Regardless of the approach, always conclude with:

Therefore, the final answer is: $oxed{answer}$. I hope it is correct.

Where [answer] is just the final number or expression that solves the problem.

Problem: The circles $C_1$ and $C_2$ are defined by the equations $x^2 + y^2 = 1$ and $(x - 2)^2 + y^2 = 16,$ respectively.  Find the locus of the centers $(a,b)$ of all circles externally tangent to $C_1$ and internally tangent to $C_2.$  Enter your answer in the form
\[Pa^2 + Qb^2 + Ra + Sb + T = 0,\]where all the coefficients are integers, $P$ is positive, and $\gcd(|P|,|Q|,|R|,|S|,|T|) = 1.$

Note: The word "locus" is a fancy word for "set" in geometry, so "the locus of the centers" means "the set of the centers".
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