Hyperbolas

This chapter has six sections. The first section deals with Basic equations of Hyperbola. Hyperbola 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 constant. We will learn first principles approach to derive the basic equation representing a hyperbola in the first section. In the second section, we will discuss about Tangents with different forms of Hyperbolas. Chords of contact, chords bisected at given points, pair of tangents from external points etc. are also discussed in this section. The third section deals with the Normals. In this section, we will discuss about Normals with different forms of Hyperbolas. The fourth section deals with Chords and Pair of Tangents. An extensive discussion on Chord of Contact, Chord Bisected, Pair of Tangents etc. in relation to different forms of Hyperbola is being done using many examples. In the fifth section, the topic on Rectangular Hyperbola is being discussed. Asymptotes are dealt with thoroughly to have a better understanding of Rectangular Hyperbolas. The equations of tangents and normal (in various forms) to a rectangular hyperbola that has been specified using its asymptotes as the coordinate axes are also being discussed. 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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