Ifthe equation `(2x-y-3)^2=-20(x +2y-4)` represents a parabola then its vertex is

y^2+2y-x+5=0 represents a parabola. Find its vertex.

Show that the equation y^2 - 8y -x+19 = 0 represents a parabola. Find its vertex, focus and directrix.

Show that the equation y^(2) - 8y - x + 19 = 0 represents a parabola . Find its vertex, focus and directrix.

The equation 2y^(2)+3y-4x-3=0 represents a parabola for which

The equation 2y^(2)+3y-4x-3=0 represents a parabola for which

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 coordinates of its vertex, the equation of its latus rectum

The equation y=x^2+2x+3 represent a parabola with its axis parallel to y-axis

Prove that the equation y^(2)+2ax+2by+c=0 represents a parabola whose axis is parallel to the axis of x. Find its vertex.

Prove that the equation y^(2)+2ax+2by+c=0 represents a parabola whose axis is parallel to the axis of x. Find its vertex.

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.