Ellipses

This chapter has five sections. The first section deals with ellipse. An ellipse is the locus of a moving point such that the ratio of its distance from a fixed point to its distance from a fixed line is a constant less than unity. Ellipse has foci and directrices each. In the second section, we learn about Tangents. The tangent of a right-angled triangle carved out of an ellipse can be defined as the ratio of the length of the opposite side to the length of the adjacent side. As in circles and parabolas, the equation of a tangent in an ellipse can take various different forms and these are discussed in this section. The third section deals more extensively on Tangents and Chords. A line segment that joins two points of an ellipse, circle or a curve is called the Chord. Diameter is the biggest chord in an ellipse, circle etc. The equations of the chord of contact chord bisected at a given point and pair of tangents from a point are dealt with extensively. The 4th section deals with Normals. In this section, finding equations for normals to ellipse is addressed. At the end of this section, we have a series of exercises to test your understanding of this chapter, solved examples, previous years’ IIT JEE questions pertaining to this chapter.

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