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Hyperbola

LEARNING OBJECTIVES

After studying this chapter, the student will be able to understand:

• Standard equation

• Parametric equation

• Foci; directrix; eccentricity, latus rectum

• Equation of auxillary and direct circle of the hyperbola

• Equation of tangent at point (x1, y1) and at θ point and the necessary and sufficient condition for y = mx + c to be a tangent to the hyperbola and the co-ordinates of point of contact

• Properties of Hyperbola

• Asymptoter and rectangular hyperbola—its equation and foci

Definition

The set of all points in the plane whose distance from a fixed point is in a constant ratio e to its distance from a fixed line is called a hyperbola and e > 1.

The fixed point is said to be focus, the fixed line is ...

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