Conic section is one of the most important parts of Mathematics in the syllabus of WBJEE entrance examination.
In this article, we come up with the chapter notes of one of the parts of the conic section i.e., Parabola including important concepts, formulae and some previous year solved questions for coming WBJEE entrance examination 2018. About 1-2 questions are always asked from this topic in the examination.
About the chapter notes:
1. These notes are based on the latest syllabus of WBJEE 2018.
2. These notes are prepared after the detailed analysis of the pattern and difficulty level of previous year papers of WBJEE examination.
3. These notes are prepared by experienced Subject Experts of Mathematics.
4. These notes will help all engineering aspirants to save their time when only few days are left before the examination.
About the Exam:
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.
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Important Concepts:
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Some previous years solved questions are given below:
Question 1:
Solution 1:
Hence, the correct option is (d).
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Question 2:
Solution 2:
Hence, the correct option is (b).
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Question 3:
Solution 3:
Hence, the correct options are (a) and (b).
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Question 4:
If y = 4x + 3 is parallel to a tangent to the parabola y^{2} = 12x, then its distance from the normal parallel to the given line is
Solution 4:
We have equation of line,
y = 4x + 3
So, slope of line = 4
Also, a = 3
Equation of normal
y = mx – 2am – am^{3}
y = 4x – 216
Hence, the correct option is (B).
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Question 5:
The point on the parabola y^{2} = 64x which is nearest to the line 4x + 3y + 35 = 0 has coordinates
(A) (9, –24)
(B) (1, 81)
(C) (4, –16)
(D) (–9, –24)
Solution 5:
The coordinate of foot of the normal are (am^{2}, –2am)
Comparing the equation of parabola with the standard equation of parabola, we get:
a = 16
We have the equation of line:
4x + 3y + 35 = 0
So, the slope of line is -4/3
So, the slope of normal to the line is 3/4.
So, the point on the parabola is (9, –24).
Hence, the correct option is (A).
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