# BITSAT Mathematics Conic Sections MCQs

Refer to BITSAT Mathematics Conic Sections MCQs provided below. BITSAT Full Syllabus Mathematics MCQs with answers available in Pdf for free download. The MCQ Questions for Full Syllabus Mathematics with answers have been prepared as per the latest syllabus, BITSAT books and examination pattern suggested in Full Syllabus by BITSAT, NCERT and KVS. Multiple Choice Questions for Conic Sections are an important part of exams for Full Syllabus Mathematics and if practiced properly can help you to get higher marks. 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 refer to the following multiple-choice questions with answers for Conic Sections in Full Syllabus. These MCQ questions with answers for Full Syllabus Mathematics will come in exams and help you to score good marks

### 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)  #### 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)

#### 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 • a) 1
• b) 2
• c) 3
• d) 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

#### 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

#### 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)  • a) –15/4
• b) –27/4
• c) –1/4
• d) –3/4

#### 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)  #### 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 • a) 2
• b) √2
• c) 2 √2
• d) 3 √2

#### is

• a) • b) • c) • d)  #### Question: The equation of the ellipse with focus at and as one directrix is

• a) • b) • c) • d) None of these • a) 16
• b) –18
• c) – 13
• d) – 10

• a) 3/2
• b) 3/4
• c) 1/10
• d) 1/20

• a) – 6
• b) 6
• c) 1/4
• d) – 1/4

#### 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 • a) y = 3
• b) y = 1
• c) y = 6
• d) y = 7

#### Question: Find the vertex of the parabola x2 – 8y – x + 19 = 0.

• a) • b) • c) • d)  #### 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)  #### 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)  #### 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

#### 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

#### 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

#### 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) √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)  #### 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

#### 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

• a) 30º
• b) 60º
• c) 90º
• d) 45º

• a) 11/4 m
• b) 8/3 m
• c) 7/2 m
• d) 2 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

## More Study Material

### BITSAT Full Syllabus Mathematics Conic Sections MCQs

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#### BITSAT MCQs Mathematics Full Syllabus Conic Sections

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Multiple Choice Questions (MCQs) for Conic Sections Full Syllabus Mathematics are objective-based questions which provide multiple answer options, and students are required to choose the correct answer from the given choices.