Ellipse - Mathematics

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• Standard form
• Problems based on finding focus, directrix, vertex, latus rectum etc.
• Position of a point w.r.t. ellipse
• Parametric coordinates
• Condition of a line to be tangent to ellipse
• Focal distance
• Equation of tangent
• Equation of normal
• Equation of chord of contact
• Equation of chord with midpoints
• Equation of pair of tangents
• Condition of a line to be tangent to parabola
• Geometrical properties
• Focal chord
• Point of intersection of tangents
• Point of intersection of normals
• Chord of contact
• Director circle
• Auxiliary circle
• Point of intersection of tangents
• Co-normal points
• Angle between the tangents
• Basing on director circle of ellipse
• Intersection of ellipse and a circle
• Equation of chord joining two points having eccentric angle