Find the value of `lambda` if the equation `9x^2+4y^2+2lambdax y+4x-2y+3=0` represents a parabola.

Find the value of lambda if the equation (x-1)^2+(y-2)^2=lambda(x+y+3)^2 represents a parabola. Also, find its focus, the equation of its directrix, the equation of its axis, the coordinates of its vertex, the equation of its latus rectum, the length of the latus rectum, and the extremities of the latus rectum.

The equation x^(2)y^(2)-9y^(2)-6x^(2)y+54y=0 represents

Find the value of lambda if 2x^2+7x y+3y^2+8x+14 y+lambda=0 represents a pair of straight lines

The second degree equation x^2+4y^2-2x-4y+2=0 represents

Does equation (5x-5)^(2)+(5y+10)^(2)=(3x+4y+5)^(2) represents a parabola ?

Find the lines whose combined equation is 6x^2+5x y-4y^2+7x+13 y-3=0

Find the value of 'k' for which the pair of equations 2x - ky + 3 = 0. 4x + 6y - 5 = 0 represent parallel lines.

9x^(2) +2hxy +4y^(2) +6x +2fy - 3 = 0 represents two parallel lines. Then

For what value of 'k'. The pair of equations 3x + 4y + 2 = 0 and 9x + 12y + k = 0 represents coincident lines.

Find the value of lambda ,if the lines 3x-4y-13=0,8x-11 y-33=0 and 2x-3y+lambda=0 are concurrent.