# 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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