Ellipse with axis not parallel to coordinate axis

Determine all terms (vertex; minor axis; major axis; focii; latus rectum centre; ordinate; double ordinate for ellipse with axis parallel to coordinate axis?

Parabola with axis parallel to coordinate axis

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.

The equation of the ellipse with its axes as the coordinate axes respectively and whose major axis =6 and minor axis =4 is

The ellipse E:(x^(2))/(25)+(y^(2))/(16)=1 is inscribed in a rectangle R whose sides are parallel to the coordinate axes. A hyperbola (with same centre and transverse axis same as major axis of ellipse) intersects the ellipse orthogonally and passes through the vertices of the rectangle.Then eccentricity of the hyperbola is

The equation of the ellipse with its axes as the coordinate axes respectively and whose minor axis =6 and eccentricity= 1/2 is

The ellipse E_(1):(x^(2))/(9)+(y^(2))/(4)=1 is inscribed in a rectangle R whose sides are parallel to the coordinates axes. Another ellipse E_(2) passing through the point (0, 4) circumscribes the rectangle R. The length (in units) of the major axis of ellipse E_(2) is

The differential equation of all parabolas with axis parallel to the axis of y is :

Rays Not Parallel To Principle Axis

Find the differential equation of all parabolas whose axis are parallel to the x-axis.