## Toppers Notes on The Hyperbola

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### Table of Content

• Definition of the hyperbola.
• Standard equation of the hyperbola.
• Conjugate hyperbola.
• The parametric form of the hyperbola.
• Position of a point with respect to the hyperbola.
• The intersection of a line and a hyperbola.
• 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 hyperbola.
• Pole and polar.
• The equation of polar.
• Properties of pole and polar.
• The diameter of the hyperbola.
• Conjugate diameters of the hyperbola.
• The properties of the diameters.
• The properties of the conjugate diameters.
• Equi-conjugate diameters.
• Subtangent and subnormal.
• Properties of the hyperbola.
• Asymptotes of the hyperbola.
• Properties of asymptotes.
• Rectangular hyperbola/Equilateral hyperbola.