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## Ellipse

##### LEARNING OBJECTIVES

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

• The standard equation and parametric equation of ellipse, the foci, directrix, eccentricity, latus rectum

• Equation of auxilliary and directries circle of the ellipse

• The equation of tangent at point (x, y,) and the necessary and sufficient condition of y = mx + c to be a tangent to the ellipse and the co-ordinates of point t.

• Properties of the ellipse

• The position of a point with respect to the ellipse.

#### Definition

Set of all points in a plane whose distance from a fixed line is said to be directrix of the ellipse and the constant ratio e (e 1) is said to be eccentricity of the ellipse.

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

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