Prove that the equation `y^(2) + 2Ax +2 By + C=0` represents a parabola, whose axis is parallel to the axis of x, and find its vertex and the equation to its latus rectum.

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

Prove that the equation y^(2)+2Ax+2By+c=0 is represent a parabola and whose axis is parabola to x axis

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

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

Equation of a parabola whose vertex is (2,-3), axis is parallel to the x axis and latus rectum 8 is

Find the differential equation of the family of parabola whose axis is parallel to X -axis and vertex is on Y -axis

The vertex of a parabola is at (4,3) and directrix is x-y+1=0. Then the equation of its latus rectum is

Find the equation to the parabola whose axis is parallel to y -axis and which passes through the points (0,4).(1,9) and (2,6) and determine its latus rectum.

Find the equation of the parabola whose focus is S(-1,1) and directrix is 4x+3y-24=0 .Also find its axis,the vertex,the length,and the equation of the latus rectum.

Find the differential equation of all parabolas whose axes are parallel to the x-axis an having latus rectum a.