If the focus and vertex of a parabola are the points (0, 2) and (0, 4), respectively, then find the equation

The coordinates of the vertex and focus of a parabola are (1,2) and (-1,2) respectively : find its equation.

If the vertex of a parabola is the point (-3,0) and the directrix is the line x+5=0 , then find its equation.

If the centre, vertex and focus of a hyperbola be (0,0), (4,0) and (6,0) respectively, then the equation of the hyperbola is

The equation of the axis and directrix of a parabola are y - 3 = 0 and x + 3 = 0 respectively and the length of the latus rectum is 8 units . Find the equation of the parabola and the coordinate of its vertex .

If the coordinates of vertex and focus of a parabola be (2,1) & (2,3) respectively, then the axis of the parabola will be

The axis of a parabola is parallel to x axis. If the the parabola passes through the point (2, 0), (1, -1) and (6, -2), then find the equation of the parabola.

The eccentricity of an ellipse is (2)/(3) and the coordinates of its focus and the corresponding vertex are (1,2) and (2,2) respectively. Find the equation of the ellipse . Also find the coordinate of the point of intersection of its major axis and the directrix in the same direction .

The vertex of a parabola is at the origin and its focus is (0,-(5)/(4)) , find the equation of the parabola.

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.

Find the equation of the tangent to the parabola y^(2)=8x at the point (2t^(2),4t) . Hence find the equation of the tangnet to this parabola, perpendicular to x+2y+7=0