Troublesome parabola

Geometry Level 4

Let s = 0 s=0 be a parabola touching the x x -axis at ( 1 , 0 ) (1,0) and y = x y=x at ( 1 , 1 ) (1,1) , respetively. Let ( a , b ) (a,b) and ( p , q ) (p,q) be the focus and the vertex of the parabola.

The slope of the axis of the parabola can be expressed as m n \dfrac mn , where m m and n n are coprime positive integers.

The equation of the directrix is d x + f y e = 0 dx + fy -e = 0 , where d , e , f d,e,f are coprime positive integers.

If p q a 2 = k \dfrac{p-q}{a^2}= k , find the value of m + n + k + d + e + f m+n+k+d+e+f .


The answer is 8.

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1 solution

Avi Solanki
Feb 11, 2017

the slope of the axis can be found using the mid point of (1,1) and (1,0)

avi solanki - 4 years, 3 months ago

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