## Toppers Notes on The Ellipse

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### Table of Content

• Definition of the ellipse.
• Standard equation of the ellipse.
• The parametric form of the ellipse.
• Position of a point with respect to the ellipse.
• The intersection of a line and an ellipse.
• Equation of tangents in different forms.
• Equation of normal in different forms.
• Auxillary circle.
• The eccentric angle of a point.
• The equation of pair of tangents.
• The director circle.
• The chord of contact.
• The equation of the chord which bisected at a given point.
• The equation of a chord joining two points on the ellipse.
• Pole and polar.
• The equation of polar.
• Properties of pole and polar.
• The diameter of the ellipse.
• Conjugate diameters of the ellipse.
• The properties of the diameters.
• The properties of the conjugate diameters.
• Equi-conjugate diameters.
• Subtangent and subnormal.
• Properties of the ellipse.