Find the equation of the parabola the extremities of whose latus rectum are (1, 2) and (1, -4).

Find the equation of the hyperbola , the length of whose latus rectum is 4 and the eccentricity is 3.

Find the equation of the parabola having (3,-6) and (3,6) as the extremities of the latus rectum .

Find the equation of hyperbola whose conjugate axis = latus-rectum = 8 ,

Find the equation of the hyperbola whose foci are (0,pm4) and latus rectum is 12.

Find the equations of normal to the parabola y^(2)=4ax at the ends of the latus rectum.

Find the equation of the parabola whose vertex is (2,3) and the equation of latus rectum is x=4. Find the co-ordinates of the point of intersection of this parabola with its latus rectum.

If the vertex =(2,0) and the extremities of the latus rectum are (3,2) and (3,-2), then the equation of the parabola is:

Find the equations of the normals at the ends of the latus-rectum of the parabola y^(2)=4ax Also prove that they are at right angles on the axis of the parabola.

Let A be the vertex and L the length of the latus rectum of the parabola,y^(2)-2y-4x-7=0 The equation of the parabola with A as vertex 2L the length of the latus rectum and the axis at right angles to that of the given curve is: