NCERT Solutions for Class 11 Maths Chapter 10 Exercise 10.4

Even though, eccentricity is not a big concepts, but one should learn the definition as it explained briefly. Here, it means it is a ratio e = c/a is eccentricity of hyperbola. But to understand the meaning of this definition one has to recall all the concepts they learned in this chapter along with the 10th class mathematics. What matter most in the fourth section of the chapter 10 from NCERT solutions for Maths class 11 is the structure of hyperbola and its features?

A hyperbola is a figure where two distinct parabola-shaped figures, whose vertex is facing each other. But do not confuse them considering as parabola because in hyperbola two shapes are sharing only one directrix and two focus points as well as an axis. These axes have positive coordinates and the other will have negative. All three figures that you have learned so far are an important part of advanced mathematics and geometry.

The real-life applications for these concepts are far vaster than you realize yet. Though, you will only study the introduction part hyperbola.

The topic “Standard equation of Hyperbola” is a lengthy topic in which you will be introduced to classification of hyperbolas and various aspects of hyperbolas, and their orientations too. One thing to remember is a hyperbola in which a = b will be counted as an equilateral hyperbola.

The standard equation of hyperbolas has transverse and conjugate axes as the coordinate axes and the center at the origin, but there are hyperbolas that have two perpendiculars with transverse and conjugate axes though you will not learn about that in class 11th mathematics.

In case of the Ellipse, it is much easier to understand the Latus rectum. Here, in case of hyperbola, it is a line segment perpendicular to the transverse axis through any of the foci given that lie on the hyperbola. This can be denoted as in example 14 you will see the question asked directly to find the coordinates of the foci, and vertices. In fact and you will be demonstrated in the solution how to calculate the length of the Latus rectum.

One of the things to notice here is that figures are not given in the example. However, you need to make the figures every time you solve the question which will eventually build the speed along with accuracy. In exercise 10.4 you will get to practice the same concept for questions 1 to 6 where the direct equation is given for the hyperbola figures and then other questions have different given conditions.