Let "ABC" be an isosceles triangle in which "A" is at `(-1,0),/_A=(2 pi)/(3),AB=AC` and "B" is on the positve "x" -axis.If `BC=4sqrt(3)` and the line "BC" intersects the line `y=x+3` at `(alpha,beta)` ,then `(beta^(4))/(alpha^(2))` is___________.

The side AB of an isosceles triangle is along the axis of X with vertices A(-1,0) and AB=AC. The equation of the side BC when /_A=120^(@) and BC=4sqrt(3) is :

The point of intersection of the pair of lines x^(2)+xy+2y^(2)-3x+2y+4=0 is (alpha,beta) then 2 alpha+beta=

The side AB of an isosceles triangle is along the axis of x with vertices A (–1, 0) and AB = AC . The equation of the side BC when angleA=120^(@) and BC=4sqrt(3) is:

If the line (x-2)/3 =(y-1)/-5 =(z+2)/2 lies in the plane x+3y - alphaz + beta=0 , then: (alpha, beta)-=

In triangle ABC ,if AB=sqrt(2),AC=sqrt(20) ,B=(3,2,0),C=(0,1,4) and D is the midpoint of BC then AD=

If alpha, beta are the roots of equation 3x^(2)-4x+2=0 , then the value of (alpha)/(beta)+(beta)/(alpha) is

Consider the equation of a pair of straight lines as x^2-3xy+lambday^2+3x=5y+2=0 The point of intersection of line is (alpha, beta) , then the value of alpha^2+beta^2 is

Consider a triangle having vertices A (-2, 3) , B (1, 9) and C ( 3, 8). If a line L passing through the circume centre of triangle ABC, bisects line BC, and intersects y – axis at point (0, (alpha )/(2)), then the value of real number alpha is ____________.