# Steiner Inellipse Problem

Geometry Level 5

The coordinates of the 3 vertices of the triangle are

$$\left( -2,-2 \right) ,\left( 6,13 \right) ,\left( 10,3 \right)$$

The implicit equation of the inscribed ellipse with the maximum possible area can be expressed in this form

$$a{ y }^{ 2 }+bxy+{ cx }^{ 2 }+dy+ex+f=0$$

where $$a, b, c, d, e, f$$ are co-prime integers, and $$a>0$$.

Find $$\sqrt { (a+b+c+d+e+f) }$$

You're welcome to check Calvin Lin's post

5 points determine a conic

or try something else.

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