If on a given base BC[B(0,0) and C(2,0)], a triangle is described such that the sum of the base angles is 4, then the equation of the locus of the opposite vertex A is parabola whose directrix is y=k. The value of k is _________ .

Answer

2.125

Explanation

(2.125)
Given `tanalpha+tanbeta=4`
`or(y)/(x)+(y)/(2-x)=4`
`ory=2x(2-x)`
`or-(y)/(2)=x^(2)-2x=(x-1)^(2)-1`
`or(x-1)^(2)=--(1)/(2)(y-2)`
Directrix: `y-2=(1)/(8)ory=(17)/(8)`