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WBJEE: Important Questions and Preparation Tips – Hyperbola

Nov 17, 2017 12:10 IST
    WBJEE 2018: Hyperbola
    WBJEE 2018: Hyperbola

    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:

    WBJEE Hyperbola concepts 1

    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) 3x2 – y2 = 48

    (B) 4x2 – y2 = 48

    (C) x2 – 3y2 = 48

    (D) x2 – 4y2 = 48

    Solution 1:

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

    The length of latus rectum of hyperbola is 2b2/a

    So,

    ae = 8                     …(1)

    Also,

    2b2/a = 24

    So,

    64 = a2 + 12a                     …(2)

    From (1) and (2),

    a = 48

    e = 1/6

    So, the equation of hyperbola is

    x2/16 – y2/48 = 1

    Or, 3x2 – y2 = 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

    WBJEE Hyperbola solution 1

    WBJEE Hyperbola solution

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

    Important Questions and Preparation Tips – Permutation and Combination

    Question 3:

    Let 16x2 – 3y2 – 32x – 12y = 44 represent a hyperbola. Then,

    WBJEE Hyperbola Solution 3

    Solution 3:

    WBJEE Hyperbola Solution 3

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

    Important Questions and Preparation Tips – Sequence and Series

    Question 4:

    WBJEE hyperbola question 4

    Solution 4:

    WBJEE hyperbola solution 4

    WBJEE Hyperbola Solution 4

    Hence, the correct option is (A).

    Important Questions and Preparation Tips – Relations and Functions

    Question 5:

    WBJEE hyperbola question 5

    Solution 5:

    WBJEE hyperbola solution 5

    Hence, the correct option is (d).

    WBJEE Mathematics Syllabus: 2017 - 2018

    WBJEE 2014 Solved Mathematics Question Paper

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