Circle in a kite.

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 $a+b+c+d+e$