Circle in a kite.

Calculus Level pending

A kite ABCD is drawn with its sides defined by the lines

\(\overline{AB}=y=-\dfrac{9}{8}x+\dfrac{227}{8}\)

\(\overline{BC}=y=\dfrac{9}{8}x-\dfrac{227}{8}\)

\(\overline{CD}=y=-2x-19\)

\(\overline{AD}=y=2x+19\)

An ellipse is drawn such that it is tangent to \(\overline{AB},\overline{BC}\) where \(x=11\) and it is tangent to \(\overline{CD},\overline{AD}\) where \(x=-3\).

If the equation of the ellipse can be represented by \(ax^2-bx+cy^2+dy-e=0\)

find \(a+b+c+d+e\)

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