Use Reflection Properties Of Parabola !

Let a parabola with focus $(5, 5)$ touches the two lines : $\displaystyle{ L }_{ 1 }:\quad y=\quad x+1, \\ { L }_{ 2 }:\quad y=-x+1.$

the equation of the parabola be : $\displaystyle\left| \frac { ax-by+c }{ \sqrt { d } } \right| \quad =\quad \sqrt { { (x-e) }^{ 2 }+{ (y-e) }^{ 2 } }.$

Find Value of $a+b+c+d+e$

Details and assumptions

• $a ,b ,c,d,e$ are all Positive integers, '$d$' is square free integer. And Don't count '$e$' twice .

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