If (0,0),(3,0) and (x,y) are the vertices of an equilateral triangle, find x and y.

Prove that the points (0, 0), (3, (pi)/(2)) and (3, (pi)/(6)) are the vertices of an equilateral triangle.

Show that the following sets of points are the vertices of an equilateral triangle :- (0,0), (5, 5sqrt3) and (-5,5sqrt3) .

If A(x_1,y_1),B(x_2,y_2),C(x_3,y_3) are the vertices of the triangle then find area of triangle

If one vertex of an equilateral triangle of side 'a' lie at the origin and the other lies on the line x-sqrt3 y = 0 , the co-ordinates of the third vertex are:

Find the locus of the vertices of equilateral triangle circumscribing the ellipse x^(2)/a^(2)+y^(2)/b^(2)=1 .

Two vertices of an equilateral triangle are (0, 0) and (0,2 sqrt3) . Find the third vertex.

Show that the lines x^2-4xy+y^2=0 and x+y=3 form an equilateral triangle and find its area.

Draw the graphs of equations : 5x - 6y + 30 = 0 , 5x + 4y - 20 = 0 Also find the vertices of the triangle formed by the above two lines and x-axis.

Draw the graphs of the equations x -y + 1 = 0 and 3x + 2y - 12 = 0. Determine the coordinates of the vertices of the triangle formed by these lines and the x-axis and shade the triangular region.

In fig. trianglePQR is an equilateral triangle with points Q(-3,0) and R(3,0). Find the coordinates of the vertex P.