- Cuemath is an online math learning platform in which students are taught one-on-one by maths professionals. Students in the Cuemath
- Students in the online classes learn math by solving problems independently under the supervision of their teacher. The teacher gently nudges the learner in the guidance of the answer if they get stuck.
- Here, with the assistance of this specific article, one will get to know a lot more about Cuemath classes. They will also get to know about Hyperbola.

**What are the Benefits a Learner Gets from Cuemath Classes?**

Now, we will be illustrating and discussing the advantages that are provided by the Cuemath classes to the learners.

- The curriculum is designed to make arithmetic learning enjoyable for the learners.
- To improve the mental sense of the learners, there are additional tab-based arithmetic games.
- Online puzzle cards are available to help improve creative reasoning and out-of-the-box thinking.
- Students in the online program learn math by solving problems independently under the supervision of their teacher.
- Cuemath speculates that each student is extraordinary, so it tailors its program to fit their learning style.

**What Do You Understand by Hyperbola?**

A hyperbola** **can be comprehended as the locus of all points in a plane whose distances from two fixed points in the plane are equal. The locus of all points in a plane whose distances from two fixed points in the plane are equal is called a hyperbola.

The hyperbola’s transverse axis is a row portion that enacts through both foci.

**What is the Standard Equation of Hyperbola?**

The standard equation of hyperbola is illustrated below;

( x*x / a*a ) – ( y*y / b*b) = 1

Here,

b*b= a*a ( e*e – 1)

**A Few Real-life Examples of Hyperbola**

Examples are a great means to grasp concepts and comprehend things. Now, here we will be illustrating a few actual existing examples. Those are listed below;

- Guitar
- Dulles Airport
- Gear Transmission
- Kobe Port Tower
- Satellite System
- Radio System
- Lens
- Monitor
- Optical Glasses

**Important Terms to Know **

Focus:- s = ( a*e, 0) and s1 = ( – a*e, 0)

Eccentricity:- This is characterized by e.

e*e = 1 + ( b*b /a*a) = 1+conjugate axis * conjugate axis / transverse axis *transverse axis

Directrix:- x = (a/e ), x= ( – a/e)

Principal axes:- The principal axes are the transverse axes and the conjugate axes.

Vertices:- H= ( a, 0) and H1= ( -a, 0)

**What Do You Understand About Conjugate Hyperbola?**

The conjugate hyperbolas can be comprehended as the two hyperbolas in which the transverse and conjugate axes of one hyperbola are the conjugate and transverse axes of the other.

We will be discussing this with the assistance of an example. The example is illustrated below:-

- (x*x / a*a ) – ( y*y / b*b ) =1

(-x*x / a*a) + ( y*y / b*b) =1

(y*y /b*b) – ( x*x / a*a ) =1

( a*a ) = b*b ( e*e – 1 )

From here, we can get the ‘e’,

The formula to get the ‘e’ is illustrated below ;

e = √1+a*a/b*b

**A few Examples of Hyperbola**

A few of the examples of hyperbola are illustrated and discussed below ;

**Example:** Get the equation of tangent to hyperbola x*x / P – y*y =1. The slope for the given question is k.

**Solution:**

This will be solved using the formula already spoken of above;

Given- slope = K

The formula is,

y= m*x + √(a*a*m*m – b*b)

We will put all the given values in the formula and get the answer.

To learn moreover about this specific theme, in a very fun and imaginative way, visit Cuemath to book a free session.