`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.

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.

In each of the following find the coordinates of the focus , axis of the parabola , the equation of the directrix and the length of the latus rectum. x^(2)=-9y

In each of the following find the coordinates of the focus , axis of the parabola , the equation of the directrix and the length of the latus rectum. x^(2)=6y

In each of the following find the coordinates of the focus , axis of the parabola , the equation of the directrix and the length of the latus rectum. y^(2)=-8x

In each of the following find the coordinates of the focus , axis of the parabola , the equation of the directrix and the length of the latus rectum. y^(2)=10x

Find the coordinates of the focus , axis, the equation of the directrix and latus rectum of the parabola y^(2)=8x .

In each of the following find the coordinates of the focus , axis of the parabola , the equation of the directrix and the length of the latus rectum. x^(2)=-16y

In each of the following find the coordinates of the focus , axis of the parabola , the equation of the directrix and the length of the latus rectum. y^(2)=12x .

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.

Find the equation of the hyperbola where foci are (0,+-12) and the length of the latus rectum is 36 .