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) 7x
^{2}– 2y^{2}+ 12xy – 2x – 14 – 22 = 0 - b) 7x
^{2}+ 2y^{2}– 12xy – 2x + 14 – 22 = 0 - c) 7x
^{2}+ 2y^{2}+ 12xy – 2x – 14 – 22 = 0 - d) 7x
^{2}– 2y^{2}+ 12xy – 2x + 14 – 22 = 0

**Answer: ****7x ^{2} – 2y^{2} + 12xy – 2x + 14 – 22 = 0**

#### Question: Find the parametric coordinates of any point of the circle x^{2} + y^{2} + 2x – 3y – 4 = 0

- a)
- b)
- c)
- d)

**Answer:**

#### Question: If the tangent at the point P(x_{1}, y_{1}) to the parabola y^{2} = 4ax meets the parabola y^{2} = 4a(x + b) at Q and R, then the mid-point of QR is

- a) (x
_{1}+ b, y_{1}+ b) - b) (x
_{1}– b, y_{1}– b) - c) (x
_{1}, y_{1}) - d) (x
_{1}+ b, y_{1})

**Answer: ****(x _{1}, y_{1})**

#### Question: If the line 3x + ay – 20 = 0 cuts the circle x^{2} + y^{2} = 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 x^{2} + y^{2} – 2x – 6y + 9 = 0 and x^{2} + y^{2} + 6x – 2y + 1 = 0, is -

- a) 1
- b) 2
- c) 3
- d) 4

**Answer: ****4**

#### Question: The equation of the tangent to the elipse x^{2} + 4y^{2} = 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 x^{2} + y^{2} = a^{2} 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 y^{2} = 8x and x^{2} + y^{2} -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 x^{2} + y^{2} + 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 y^{2} = 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 x^{2} + y^{2} + 2fy + λ = 0 to the circle x^{2}+ y^{2} + 2fy + μ = 0, where μ > λ > 0, is

- a)
- b)
- c)
- d) μ + λ

**Answer:**

#### Question: Find the eccentricity of the conic represented by x^{2} – y^{2} – 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 x^{2} + y^{2} + 5x + 3y +7 = 0 and x^{2} + y^{2} – 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 y^{2} – 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 cx^{2} + dy^{2} = 1 only once if

- a) ca
^{ 2}+ db^{2}=1 - b)
- c)
- d) ac
^{2}+ bd^{2}= 1

**Answer:**

#### Question: Find the equation of chord of the circle x^{2} + y^{2}= 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 x^{2} – 8y – x + 19 = 0.

- a)
- b)
- c)
- d)

**Answer:**

#### Question: Which of the following lines, is a normal to the parabola y^{2} = 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 9x^{2} + 16y^{2} =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 x^{2} + y^{2} = a^{2} 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 y^{2} = 8x and x^{2} + y^{2} -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 x^{2} + y^{2} + 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 15x^{2} +15y^{2} - 48x + 64y = 0 to the two circles 5x^{2} + 5y^{2} – 24x + 32y + 75 = 0 and 5x^{2} + 5y^{2} – 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 x^{2} + y^{2} - 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 y^{2} = 4ax, which are at right angle to one another is

- a) x
^{2}+ y^{2}= a^{2} - b) ay
^{2}=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 y^{2} = 8x and PQ be the common chord of the circle x^{2} + y^{2} – 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) 4x
^{2}+ 3y^{2}= 1 - b) 3x
^{2}+ 4y^{2}= 12 - c) 4x
^{2}+ 3y^{2}= 12 - d) 3x
^{2}+ 4y^{2}= 1

**Answer: ****3x ^{2} + 4y^{2} = 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 x^{2} + y^{2} – 2x – 2y = 0 and x^{2} + y^{2} = 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 x^{2} + y^{2}+ 20 (x + y) + 20 = 0, then the equation of the pair of tangent are

- a) x
^{2}+ y^{2}- 5xy = 0 - b) x
^{2}+ y^{2}+ 2x + y = 0 - c) x
^{2}+ y^{2}– xy + 7 = 0 - d) 2x
^{2}+ 2y^{2}+ 5xy = 0

**Answer: ****2x ^{2} + 2y^{2} + 5xy = 0**

## More Study Material

### BITSAT Full Syllabus Mathematics Conic Sections MCQs

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Regular MCQs practice helps to gain more practice in solving questions to obtain a more comprehensive understanding of Conic Sections concepts. MCQs play an important role in developing understanding of Conic Sections in BITSAT Full Syllabus. Students can download and save or print all the MCQs, printable assignments, practice sheets of the above chapter in Full Syllabus Mathematics in Pdf format from studiestoday. You can print or read them online on your computer or mobile or any other device. After solving these you should also refer to Full Syllabus Mathematics MCQ Test for the same chapter

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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.