HyperbolaWe have studied earlier about parabolas and ellipses as two conic sections. In this chapter we will study another conic section called hyperbola which can be obtained by cutting a right circular come at both the nappe by a plane. Thus it has two branches, one on each nappe.

Hyperbolais the locus of a point which moves in a plane such that it distance from a fixed point is e(>1) times its distance from a fixed straight line. It is symmetrical about two axes and one branch is the reflection of other about one of the axes. Since, we have studied ellipse in the previous chapter, it will be easier to understand this chapter. We will give you a proportion by which you can easily get the formulae for hyperbola if you know the formulae for ellipse.Most of the

properties of hyperbolaare similar to those of the ellipse. We will introduce the concept of asymptotes. You will also learn about rectangular hyperbolas and conjugate hyperbola.The

rectangular hyperbolacan be very simply represented in a parametric form. It is advisable that this fact should always be kept in the fore while solving problems on and related to rectangular hyperbola.Wishing you “All the Best” for the preparation

Hyperbolawith askIITians.com.

Topics Covered:

**Basic Concepts of Hyperbola****Relation between Focal Distances****Parametric Coordinates****Important Properties of Hyperbola****Examples Based on Hyperbola****Ellipse Vs Hyperbola****Propositions of Hyperbola****Examples on Propositions of Hyperbola****Rectangular Hyperbola****Intersection of Circle and Rectangular Hyperbola****Conjugate Hyperbola****Examples on Finding Locus of Point****Solved Examples on Hyperbola Part-I****Solved Examples of Hyperbola Part-II****Solved Examples of Hyperbola Part-III**