Derive an equation to find distance of a point on ellipse to the focus of ellipse.

Derive an equation to find angle between two intersecting ellipses.

Consider the ellipse that satisfies the following properties: major axis is vertical,length of major axis is twice the length of the minor axis ,graph passes through the vertex of the parabola with equation (y-1)^(2)=4x-2 Find an equation of the ellipse.Find the center-to-focus distance of the ellipse.

Find the equation of the ellipse from the following data: axis is coincident with x = 1, centre (1, 5), focus is (1, 8) and the sum of the focal distances of a point on the ellipse is 12.]

Consider the following ellipse: Find the equation of the ellipse.

Find the eccentricity and equations of the directrices of the ellipse (x^(2))/(100) + (y^(2))/ (36) = 1 . Show that the sum of the focal distances of any point on this ellipse is constant .

If the foci of an ellipse are (0,+-1) and the minor axis is of unit length, then find the equation of the ellipse. The axes of ellipse are the coordinate axes.

If the foci of an ellipse are (0,+-1) and the minor axis is of unit length, then find the equation of the ellipse. The axes of ellipse are the coordinate axes.

Q is a point on the auxiliary circle of an ellipse. P is the corresponding point on ellipse. N is the foot of perpendicular from focus S, to the tangent of auxiliary circle at Q. Then