If the focus of a parabola is (2, 3) and its latus rectum is 8, then find the locus of the vertex of the parabola.

If the focus of a parabola is (3,3) and its directrix is 3x-4y=2 then the length of its latus rectum is

A parabola of latus rectum l touches a fixed equal parabola. The axes of two parabolas are parallel. Then find the locus of the vertex of the moving parabola.

If focus of the parabola is (3, 0) and length of latus rectum is 8, then its vertex is [1] (2,0) [2] (1,0) [3] (0,0) [4](1,0)

If parabola of latus rectum l touches a fixed equal parabola, the axes of the two curves being parallel, then the locus of the vertex of the moving curve is

If the vertex and focus of a parabola are (3,3) and (-3,3) respectively, then its equation is

The locus of the midpoint of the focal distance of a variable point moving on theparabola y^2=4a x is a parabola whose (a)latus rectum is half the latus rectum of the original parabola (b)vertex is (a/2,0) (c)directrix is y-axis. (d)focus has coordinates (a, 0)

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.

Let y=3x-8 be the equation of the tangent at the point (7, 13 ) lying on a parabola whose focus is at (-1,-1). Find the equation of directrix and the length of the latus rectum of the parabola.

Find the equation of the parabola with focus (5, 0), and directrix x = -5 . Also, find the length of the latus rectum.

Find the equation of parabola whose Vertex is (2,3) latus rectum is 8 and axis is parallel to x-axis