Ellipse Identification

Calculus Level 5

An ellipse having the equation,

\[ \dfrac{(x - h)^2 }{ a^2} +\dfrac{ (y - k)^2 }{ b^2} = 1 \]

passes through the points \( (7, 2) \) and \( (-1, 4) \). It has a slope of \( -4 \) and \( \dfrac{1}{3} \) at the first point and second point, respectively.

Identify this ellipse, by finding \( a, b, h, k \). Enter your answer as \( a + b + h + k \).

Round your answer to three decimal places.

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