Use Reflection Properties Of Parabola !
Geometry
Level
5
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 .
Original
by
Deepanshu Gupta