West Bengal Joint Entrance Examination (WBJEE) is a state level common entrance test organized by West Bengal Joint Entrance Examinations Board for admission to the Undergraduate Level Engineering and Medical Courses through a common entrance test in the State of West Bengal.

In this article, the engineering section of Jagranjosh brings to you concise chapter notes of chapter Hyperbola based on the latest syllabus for WBJEE Entrance Examination 2018.

**About the Chapter Notes:**

In these notes you will find all important topics of chapter Hyperbola like standard equation of hyperbola, equilateral hyperbola, foci, eccentricity, length of latus rectum, equation of tangent to the hyperbola, equation of normal to the hyperbola etc.

These chapter notes are prepared after the detailed analysis of previous year papers of WBJEE Examination. These chapter notes consist of all important concepts, formulae and some previous year solved questions.

About** 2-3 questions** are always asked from this topic in WBJEE Examination.

**Important Questions and Preparation Tips – Ellipse**

**Important Concepts:**

**Important Questions and Preparation Tips – Probability**

**Some previous years solved questions are given below:**

** **

**Question 1:**

The equation of hyperbola whose coordinates of the foci are (±8, 0) and the length of latus rectum is 24 units, is

(A) 3x^{2} – y^{2} = 48

(B) 4x^{2} – y^{2} = 48

(C) x^{2} – 3y^{2} = 48

(D) x^{2} – 4y^{2} = 48

**Solution 1:**

The coordinates of foci of hyperbola are (±ae, 0)

The length of latus rectum of hyperbola is 2b^{2}/a

So,

ae = 8 …(1)

Also,

2b^{2}/a = 24

So,

64 = a^{2} + 12a …(2)

From (1) and (2),

a = 48

e = 1/6

So, the equation of hyperbola is

x^{2}/16 – y^{2}/48 = 1

Or, 3x^{2} – y^{2} = 48

Hence, the correct option is (A).

**Important Questions and Preparation Tips – Binomial Theorem**

**Question 2:**

If the straight line (*a* – 1)*x* – *by* + 4 = 0 is normal to the hyperbola xy = 1 then which of the followings does not hold?

(A) *a* > 1, *b* > 0

(B) *a* > 1, *b* < 0

(C) *a* < 1, *b* < 0

(D) *a* < 1, *b* > 0

**Solution 2:**

We have the equation of hyperbola,

xy = 1

The slope of hyperbola is given by *dy*/*dx*

Hence, the correct options are (A) and (C).

**Important Questions and Preparation Tips – Permutation and Combination**

**Question 3:**

Let 16*x*^{2} – 3*y*^{2} – 32*x* – 12*y* = 44 represent a hyperbola. Then,

**Solution 3:**

Hence, the correct options are (A), (B) and (C).

**Important Questions and Preparation Tips – Sequence and Series**

**Question 4:**

**Solution 4:**

Hence, the correct option is (A).

**Important Questions and Preparation Tips – Relations and Functions**

**Question 5:**

**Solution 5:**

Hence, the correct option is (d).