Conic Section

Find the equation of an ellipse, the distance between whose foci is 5 units and the distance between the directrices is 20 units.

Find the equation of an ellipse whose eccentricity is 2/3, the lams rectum is 5 and centre is at the origin.

Find the equation of the ellipse whose axes are along coordinate axes and passing through the points (4,3) and (-1,4).

If parabola y2 = A ax passes through the point (3,4), find the value of a.

Find equation of a parabola with vertex at origin and focus at (3,0).

Find the vertex, axis, latus rectum, focus and directrix of the parabola y2 - 8y - x +19=0. Also draw its rough sketch.