Parabolas, ellipses, and hyperbolas, oh my! Learn about this eccentric bunch of shapes.

For an ellipse \(E\) with foci \(A=(2,0)\) and \(B=(10,0),\) every point \(P\) on \(E\) satisfies \( \lvert PA \rvert + \lvert PB \rvert = 30.\) What is the equation of ellipse \(E?\)

Note: \( \lvert PA \rvert\) denotes the length of line segment \(PA\).

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