Download BITSAT MCQs for BITSAT Mathematics: Conic Sections
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Chapter-wise Objective Questions: Conic Sections
View or download the dedicated Conic Sections MCQ resource below. Practicing these 50 objective questions regularly builds familiarity with standard exam patterns and helps secure higher marks in final Mathematics evaluations.
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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