Use Reflection Properties Of Parabola !

Geometry Level 5

Let a parabola with focus (5,5) (5, 5) touches the two lines : L1:y=x+1,L2:y=x+1.\displaystyle{ L }_{ 1 }:\quad y=\quad x+1, \\ { L }_{ 2 }:\quad y=-x+1.

the equation of the parabola be : axby+cd=(xe)2+(ye)2.\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+ea+b+c+d+e

Details and assumptions

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