Practice BITSAT Mathematics Conic Sections MCQs provided below. The MCQ Questions for Full Syllabus Conic Sections Mathematics with answers and follow the latest BITSAT/ NCERT and KVS patterns. Refer to more Chapter-wise MCQs for BITSAT Full Syllabus Mathematics and also download more latest study material for all subjects
MCQ for Full Syllabus Mathematics Conic Sections
Full Syllabus Mathematics students should review the 50 questions and answers to strengthen understanding of core concepts in Conic Sections
Conic Sections MCQ Questions Full Syllabus Mathematics with Answers
Question: Find the equation of the hyperbola whose directrix is 2x + y = 1, focus (1, 2) and eccentricity √3
- a) 7x2 – 2y2 + 12xy – 2x – 14 – 22 = 0
- b) 7x2 + 2y2 – 12xy – 2x + 14 – 22 = 0
- c) 7x2 + 2y2 + 12xy – 2x – 14 – 22 = 0
- d) 7x2 – 2y2 + 12xy – 2x + 14 – 22 = 0
Answer: 7x2 – 2y2 + 12xy – 2x + 14 – 22 = 0
Question: Find the parametric coordinates of any point of the circle x2 + y2 + 2x – 3y – 4 = 0
- a)
- b)
- c)
- d)
Answer:
Question: If the tangent at the point P(x1, y1) to the parabola y2 = 4ax meets the parabola y2 = 4a(x + b) at Q and R, then the mid-point of QR is
- a) (x1 + b, y1 + b)
- b) (x1 – b, y1 – b)
- c) (x1, y1)
- d) (x1 + b, y1)
Answer: (x1, y1)
Question: If the line 3x + ay – 20 = 0 cuts the circle x2 + y2 = 25 at real distinct or coincident points, then a belongs to the interval
- a) [- √7, √7]
- b) (- √7, 1/7)
- c)
- d) None of these
Answer:
Question: The total number of common tangents to the two circles x2 + y2 – 2x – 6y + 9 = 0 and x2 + y2 + 6x – 2y + 1 = 0, is -
- a) 1
- b) 2
- c) 3
- d) 4
Answer: 4
Question: The equation of the tangent to the elipse x2 + 4y2 = 25 at the point whose ordinate is 2 is
- a) x + 2y = 5 or 2x - y = 5
- b) 3x +8y = 25 or 8y -3x = 25
- c) 3x + 2y =15 or 3y - 2x =15
- d) None of these
Answer: 3x +8y = 25 or 8y -3x = 25
Question: An equilateral triangle is inscribed in the circle x2 + y2 = a2 with one of the vertices at (a, 0). What is the equation of the side opposite to this vertex ?
- a) 2x – a = 0
- b) x + a = 0
- c) 2x + a = 0
- d) 3x – 2a = 0
Answer: 2x + a = 0
Question: The equation of one of the common tangents to the parabola y2 = 8x and x2 + y2 -12x + 4 = 0 is
- a) y = –x + 2
- b) y = x – 2
- c) y = x + 2
- d) None of these
Answer: y = x + 2
Question: The line joining (5, 0) to ( (10cos θ, 10sin θ) is divided internally in the ratio 2 : 3 at P. If θ varies, then the locus of P is
- a) A pair of straight
- b) A circle lines
- c) A straight line
- d) None of these
Answer: A circle lines
Question: The number of integral values of λ for which x2 + y2 + λx + (1- λ)y + 5 = 0 is the equation of a circle whose radius cannot exceed 5, is
- a) 14
- b) 18
- c) 16
- d) None of these
Answer: 16
Question: An ellipse has OB as semi minor axis, F and F ' its focii and the angle FBF ' is a right angle. Then the eccentricity of the ellipse is
- a)
- b)
- c)
- d)
Answer:
Question: If the line 2x – 3y = k touches the parabola y2 = 6x, then find the value of k
- a) –15/4
- b) –27/4
- c) –1/4
- d) –3/4
Answer: –27/4
Question: S and T are the foci of an ellipse and B is an end of the minor axis. If STB is an equilateral triangle, then the eccentricity of the ellipse is
- a)
- b)
- c)
- d)
Answer:
Question: The length of the tangent drawn from any point on the circle x2 + y2 + 2fy + λ = 0 to the circle x2+ y2 + 2fy + μ = 0, where μ > λ > 0, is
- a)
- b)
- c)
- d) μ + λ
Answer:
Question: Find the eccentricity of the conic represented by x2 – y2 – 4x + 4y + 16 = 0
- a) 2
- b) √2
- c) 2 √2
- d) 3 √2
Answer: √2
Question: The length of the latus-rectum of the parabola whose focus is
and directrix is
is
- a)
- b)
- c)
- d)
Answer:
Question: The equation of the ellipse with focus at 
and 
as one directrix is
- a)
- b)
- c)
- d) None of these
Answer:
Question: For what value of k the circles x2 + y2 + 5x + 3y +7 = 0 and x2 + y2 – 8x + 6y + k = 0 cuts orthogonally
- a) 16
- b) –18
- c) – 13
- d) – 10
Answer: –18
Question: If the lines 3x – 4y + 4 = 0 and 6x – 8y – 7 = 0 are tangents to a circle, then the radius of the circle is
- a) 3/2
- b) 3/4
- c) 1/10
- d) 1/20
Answer: 3/4
Question: If the line 2x – 1 = 0 is the directrix of the parabola y2 – kx + 6 = 0 then one of the values of k is
- a) – 6
- b) 6
- c) 1/4
- d) – 1/4
Answer: – 6
Question: The line ax + by = 1 cuts ellipse cx2 + dy2 = 1 only once if
- a) ca 2 + db2 =1
- b)
- c)
- d) ac2 + bd2 = 1
Answer:
Question: Find the equation of chord of the circle x2 + y2= 8x bisected at the point (4, 3)
- a) y = 3
- b) y = 1
- c) y = 6
- d) y = 7
Answer: y = 3
Question: Find the vertex of the parabola x2 – 8y – x + 19 = 0.
- a)
- b)
- c)
- d)
Answer:
Question: Which of the following lines, is a normal to the parabola y2 = 16x ?
- a) y = x – 11 cosθ – 3 cos3θ
- b) y = x – 11 cosθ – cos3θ
- c) y = (x – 11) cosθ + cos3θ
- d) y = (x – 11) cosθ – cos3θ
Answer: y = (x – 11) cosθ – cos3θ
Question: For what value of λ does the line y = x + λ touches the ellipse 9x2 + 16y2 =144.
- a)
- b)
- c)
- d)
Answer:
Question: The length of the semi-latus rectum of an ellipse is one thrid of its major axis, its eccentricity would be
- a)
- b)
- c)
- d)
Answer:
Question: An equilateral triangle is inscribed in the circle x2 + y2 = a2 with one of the vertices at (a, 0). What is the equation of the side opposite to this vertex ?
- a) 2x – a = 0
- b) x + a = 0
- c) 2x + a = 0
- d) 3x – 2a = 0
Answer: 2x + a = 0
Question: The equation of one of the common tangents to the parabola y2 = 8x and x2 + y2 -12x + 4 = 0 is
- a) y = –x + 2
- b) y = x – 2
- c) y = x + 2
- d) None of these
Answer: y = x + 2
Question: The line joining (5, 0) to ( (10cos q, 10sin q) is divided internally in the ratio 2 : 3 at P. If θ varies, then the locus of P is
- a) A pair of straight
- b) A circle lines
- c) A straight line
- d) None of these
Answer: A circle lines
Question: The number of integral values of λ for which x2 + y2 + λx + (1- λ)y + 5 = 0 is the equation of a circle whose radius cannot exceed 5, is
- a) 14
- b) 18
- c) 16
- d) None of these
Answer: 16
Question: The lengths of the tangent drawn from any point on the circle 15x2 +15y2 - 48x + 64y = 0 to the two circles 5x2 + 5y2 – 24x + 32y + 75 = 0 and 5x2 + 5y2 – 48x + 64y + 300 = 0 are in the ratio of
- a) 1 : 2
- b) 18
- c) 16
- d) None of these
Answer: 1 : 2
Question: The length of the chord x + y = 3 intercepted by the circle x2 + y2 - 2x - 2y - 2 = 0 is
- a)
- b)
- c)
√14
- d)
Answer:
√14
Question: The locus of the point of intersection of two tangents to the parabola y2 = 4ax, which are at right angle to one another is
- a) x2 + y2 = a2
- b) ay2 =x
- c) x + a = 0
- d)
Answer: x + a = 0
Question: The parabola having its focus at (3, 2) and directrix along the y-axis has its vertex at
- a) (2, 2)
- b)
- c)
- d)
Answer:
Question: Let S be the focus of the parabola y2 = 8x and PQ be the common chord of the circle x2 + y2 – 2x – 4y = 0 and the given parabola. The area of ΔPQS is
- a) 4 sq units
- b) 3 sq units
- c) 2 sq units
- d) 8 sq units
Answer: 4 sq units
Question: The eccentricity of an ellipse, with its centre at the origin, is 1/2. If one of the directrices is x = 4 , then the equation of the ellipse is:[
- a) 4x2 + 3y2 = 1
- b) 3x2 + 4y2 = 12
- c) 4x2 + 3y2 = 12
- d) 3x2 + 4y2 = 1
Answer: 3x2 + 4y2 = 12
Question: Area of the circle in which a chord of length √2 makes an angle p/2 at the centre, is
- a) π/2 sq units
- b) 2π sq units
- c) π sq units
- d) π/4 sq units
Answer: π sq units
Question: The angle of intersection of the two circles x2 + y2 – 2x – 2y = 0 and x2 + y2 = 4, is
- a) 30º
- b) 60º
- c) 90º
- d) 45º
Answer: 45º
Question: An arch of a bridge is semi-elliptical with major axis horizontal. If the length the base is 9 meter and the highest part of the bridge is 3 meter from the horizontal; the best approximation of the height of the arch. 2 meter from the centre of the base is
- a) 11/4 m
- b) 8/3 m
- c) 7/2 m
- d) 2 m
Answer: 8/3 m
Question: A pair of tangents are drawn from the origin to the circle x2 + y2+ 20 (x + y) + 20 = 0, then the equation of the pair of tangent are
- a) x2 + y2 - 5xy = 0
- b) x2 + y2 + 2x + y = 0
- c) x2 + y2 – xy + 7 = 0
- d) 2x2 + 2y2 + 5xy = 0
Answer: 2x2 + 2y2 + 5xy = 0
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Important Practice Resources for BITSAT Mathematics
MCQs for Conic Sections Mathematics Full Syllabus
Students can use these MCQs for Conic Sections to quickly test their knowledge of the chapter. These multiple-choice questions have been designed as per the latest syllabus for Full Syllabus Mathematics released by BITSAT. Our expert teachers suggest that you should practice daily and solving these objective questions of Conic Sections to understand the important concepts and better marks in your school tests.
Conic Sections NCERT Based Objective Questions
Our expert teachers have designed these Mathematics MCQs based on the official NCERT book for Full Syllabus. We have identified all questions from the most important topics that are always asked in exams. After solving these, please compare your choices with our provided answers. For better understanding of Conic Sections, you should also refer to our NCERT solutions for Full Syllabus Mathematics created by our team.
Online Practice and Revision for Conic Sections Mathematics
To prepare for your exams you should also take the Full Syllabus Mathematics MCQ Test for this chapter on our website. This will help you improve your speed and accuracy and its also free for you. Regular revision of these Mathematics topics will make you an expert in all important chapters of your course.
You can get most exhaustive BITSAT Mathematics Conic Sections MCQs for free on StudiesToday.com. These MCQs for Full Syllabus Mathematics are updated for the 2025-26 academic session as per BITSAT examination standards.
Yes, our BITSAT Mathematics Conic Sections MCQs include the latest type of questions, such as Assertion-Reasoning and Case-based MCQs. 50% of the BITSAT paper is now competency-based.
By solving our BITSAT Mathematics Conic Sections MCQs, Full Syllabus students can improve their accuracy and speed which is important as objective questions provide a chance to secure 100% marks in the Mathematics.
Yes, Mathematics MCQs for Full Syllabus have answer key and brief explanations to help students understand logic behind the correct option as its important for 2026 competency-focused BITSAT exams.
Yes, you can also access online interactive tests for BITSAT Mathematics Conic Sections MCQs on StudiesToday.com as they provide instant answers and score to help you track your progress in Mathematics.