If the point (2, 3) is the focus and x = 2y + 6 is the directrix of a parabola, find
(i) The equation of the axis.
(ii) The co-ordinates of the vertex.
(iii) Length of the latus rectum.
(iv) Equation of the latus rectum.

The equation of the latus rectum of a parabola is x+y=8 and the equation of the tangent at the vertex is x+y=12. Then find the length of the latus rectum.

The equation of the latus rectum of a parabola is x+y=8 and the equation of the tangent at the vertex is x+y=12. Then find the length of the latus rectum.

The length of the latus rectum of 3x^(2) - 2y^(2) =6 is

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.

For the hyperbola, 3y^(2) - x^(2) = 3 . Find the co-ordinates of the foci and vertices, eccentricity and length of the latus rectum.

For each of that parabolas, find the coordinates of the focus, the equation of the directrix and the length of latus rectum : x^2 = 6y

If the parabola y^(2)=4ax passes through the point (2,-3) then find the co-ordinates of the focus and the length of latus rectum.

The length of the latus rectum of the parabola x^(2) = -28y is

y^2+2y-x+5=0 represents a parabola. Find its vertex, equation of axis, equation of latus rectum, coordinates of the focus, equation of the directrix, extremities of the latus rectum, and the length of the latus rectum.

y^2+2y-x+5=0 represents a parabola. Find its vertex, equation of axis, equation of latus rectum, coordinates of the focus, equation of the directrix, extremities of the latus rectum, and the length of the latus rectum.