CBSE Class 11 Conic Section Worksheet A

Question. The largest value of r for which the region represented by the set {ω ∈ C|ω – 4 – i| ≤ r} is contained in the region represented by the set (z ≤ c / | z -1|≤| z + i |), is equal to: 
(a) 5/2 √2
(b) 2√2
(c) 3/2 √2
(d) √17
Answer : A

Question. Equation of a common tangent to the circle, x² + y² – 6x = 0 and the parabola, y² = 4x, is :
(a) 2√3y = 12x + 1
(b) √3y = x + 3
(c) 2√3y = – x – 12
(d) √3y = 3x + 1
Answer : B

Question. If y = mx + c is the normal at a point on the parabola y² = 8x whose focal distance is 8 units, then |c| is equal to :
(a) 2√3
(b) 8√3
(c) 10√3
(d) 16√3
Answer : C

Question. Let O be the vertex and Q be any point on the parabola, x² = 8y. If the point P divides the line segment OQ internally in the ratio 1 : 3, then locus of P is :
(a) y² = 2x
(b) x² = 2y
(c) x² = y
(d) y² = x
Answer : B

Question. A chord is drawn through the focus of the parabola y² = 6x such that its distance from the vertex of this parabola is √5/2 , then its slope can be:
(a) √5/2
(b) √3/2
(c) 2/√5
(d) 2/√3
Answer : A

Question. Two tangents are drawn from a point (– 2, – 1) to the curve, y² = 4x. If a is the angle between them, then |tan a| is equal to:
(a) 1/3
(b) 1/√3
(c) √3
(d) 3
Answer : D

Question. If the common tangents to the parabola, x² = 4y and the circle, x² + y² = 4 intersect at the point P, then the distance of P from the origin, is :
(a) √2+1
(b) 2(3 + 2√2)
(c) 2(√2 +1)
(d) 3 + 2√2
Answer : C

Question. Let A (4, – 4) and B (9, 6) be points on the parabola, y² = 4x. Let C be chosen on the arc AOB of the parabola, where O is the origin, such that the area of ΔACB is maximum. Then, the area (in sq. units) of ΔACB, is:
(a) 31(1/4)
(b) 30(1/2)
(c) 32
(d) 31(3/4)
Answer : A

Question. The shortest distance between the line y = x and the curve y² = x – 2 is :
(a) 2
(b) 7/8
(c) 7/4√2
(d) 11/4√2
Answer : C

Question. The equation of a tangent to the parabola, x² = 8y, which makes an angle q with the positive direction of x-axis, is :
(a) y = x tanθ + 2 cotθ
(b) y = x tanθ – 2 cotθ
(c) x = y cotθ + 2 tanθ
(d) x = y cotθ – 2 tanθ
Answer : C

Question. The length of the chord of the parabola x² = 4y having equation x - √2y + 4√2 = 0 is:
(a) 3√2
(b) 2√11
(c) 8√2
(d) 6√3
Answer : D

Question. Tangent and normal are drawn at P(16, 16) on the parabola y² = 16x , which intersect the axis of the parabola at A and B, respectively. If C is the centre of the circle through the points P, A and B and ∠CPB = θ , then a value of tan θ is:
(a) 2
(b) 3
(c) 4/3
(d) 1/2
Answer : A

Question. Let PQ be a double ordinate of the parabola, y² = – 4x, where P lies in the second quadrant. If R divides PQ in the ratio 2 : 1 then the locus of R is :
(a) 3y² = – 2x
(b) 3y² = 2x
(c) 9y² = 4x
(d) 9y² = – 4x
Answer : D

Question. The slope of the line touching both the parabolas y² = 4x and x² = -32y is
(a) 1/8
(b) 2/3
(c) 1/2
(d) 3/2
Answer : C

Question. P and Q are two distinct points on the parabola, y² = 4x, with parameters t and t1 respectively. If the normal at P passes through Q, then the minimum value of 2
t1 is :
(a) 8
(b) 4
(c) 6
(d) 2
Answer : A

Question. Let L₁ be the length of the common chord of the curves x² + y² = 9 and y² = 8x, and L₂ be the length of the latus rectum of y² = 8x, then:
(a) L₁ > L₂
(b) L₁ = L₁
(c) L₁ < L₂
(d) L_{1 /} L₂ √2
Answer : C

Question. The normal at (2, 3/2) to the ellipse, x²/16 + y²/3 = 1 touches a parabola, whose equation is 
(a) y² = – 104 x
(b) y² = 14 x
(c) y² = 26x
(d) y² = – 14x
Answer : A

Question. The chord PQ of the parabola y² = x, where one end P of the chord is at point (4, – 2), is perpendicular to the axis of the parabola. Then the slope of the normal at Q is
(a) – 4
(b) - 1/4
(c) 4
(d) 1/4
Answer : A

Question. Statement-1: The line x – 2y = 2 meets the parabola, y² + 2x = 0 only at the point (– 2, – 2).
Statement-2: The line mx - 1/2m (m ≠ 0) is tangent to the parabola, y² = – 2x at the point (- 1/2m², - 1/m).
(a) Statement-1 is true; Statement-2 is false.
(b) Statement-1 is true; Statement-2 is true; Statement-2 is a correct explanation for statement-1.
(c) Statement-1 is false; Statement-2 is true.
(d) Statement-1 a true; Statement-2 is true; Statement-2 is not a correct explanation for statement-1.
Answer : B

Question. If two tangents drawn from a point P to the parabola y² = 4x are at right angles, then the locus of P is
(a) 2x + 1 = 0
(b) x = – 1
(c) 2x – 1 = 0
(d) x = 1
Answer : B

Question. A hyperbola having the transverse axis of length 2 has the same foci as that of the ellipse 3x² + 4y² = 12, then this hyperbola does not pass through which of the following points?
(a) (1/√2, 0)
(b) (-√3/2, 1)
(c) (1,- 1/√2)
(d) (3/2, - 1/√2)
Answer : D

Question. If the point (1, 4) lies inside the circle x² + y² – 6x – 10y + P = 0 and the circle does not touch or intersect the coordinate axes, then the set of all possible values of P is the interval: 
(a) (0, 25)
(b) (25, 39)
(c) (9, 25)
(d) (25, 29)
Answer : D

Question. Let a and b be any two numbers satisfying 1/a² + 1/b² = 1/4 
Then, the foot of perpendicular from the origin on the variable line, x/a + b/b = 1, lies on: 
(a) a hyperbola with each semi-axis = √2
(b) a hyperbola with each semi-axis = 2
(c) a circle of radius = 2
(d) a circle of radius = √2
Answer : C

Question. Let C be the circle with centre at (1, 1) and radius = 1. If T is the circle centred at (0, y), passing through origin and touching the circle C externally, then the radius of T is equal to 
(a) 1/2
(b) 1/4
(c) 3/2
(d) 3/2
Answer : B

Question. The equation of circle described on the chord 3x + y + 5 = 0 of the circle x² + y²= 16 as diameter is:
(a) x² + y² + 3x + y – 11 = 0
(b) x² + y² + 3x + y + 1 = 0
(c) x² + y² + 3x + y – 2 = 0
(d) x² + y² + 3x + y – 22 = 0
Answer : A

Question. For the two circles x² + y² = 16 and x² + y² – 2y = 0, there is/are
(a) one pair of common tangents
(b) two pair of common tangents
(c) three pair of common tangents
(d) no common tangent
Answer : D

Question. If the incentre of an equilateral triangle is (1, 1) and the equation of its one side is 3x + 4y + 3 = 0, then the equation of the circumcircle of this triangle is :
(a) x² + y² – 2x – 2y – 14 = 0
(b) x² + y² – 2x – 2y – 2 = 0
(c) x² + y² – 2x – 2y + 2 = 0
(d) x² + y² – 2x – 2y – 7 = 0
Answer : A

Question. If a circle passing through the point (–1, 0) touches yaxis at (0, 2), then the length of the chord of the circle along the x-axis is :
(a) 3/2
(b) 3
(c) 5/2
(d) 5
Answer : B

Question. Let the tangents drawn to the circle, x² + y² = 16 from the point P(0, h) meet the x-axis at point A and B. If the area of ΔAPB is minimum, then h is equal to :
(a) 4√2
(b) 3√3
(c) 3√2
(d) 4√3
Answer : A

Question. If y + 3x = 0 is the equation of a chord of the circle, x² + y² – 30x = 0, then the equation of the circle with this chord as diameter is :
(a) x² + y² + 3x + 9y = 0
(b) x² + y² + 3x – 9y = 0
(c) x² + y² – 3x – 9y = 0
(d) x² + y² – 3x + 9y = 0
Answer : D

Question. If the line y = mx + 1 meets the circle x² + y² + 3x = 0 in two points equidistant from and on opposite sides of x-axis, then
(a) 3m + 2 = 0
(b) 3m – 2 = 0
(c) 2m + 3 = 0
(d) 2m – 3 = 0
Answer : B

Question. If three distinct points A, B, C are given in the 2-dimensional coordinate plane such that the ratio of the distance of each one of them from the point (1, 0) to the distance from (– 1, 0) is equal to 1/2, then the circumcentre of the triangle ABC is at the point
(a) (5/3, 0)
(b) (0, 0)
(c) (1/3, 0)
(d) (3, 0)
Answer : A

Question. If a circle of unit radius is divided into two parts by an arc of another circle subtending an angle 60 on the circumference of the first circle, then the radius of the arc is:
(a) √3
(b) 1/2
(c) 1
(d) √2
Answer : A

Question. Statement 1: The only circle having radius √10 and a diameter along line 2x + y = 5 is x² + y² – 6x + 2y = 0.
Statement 2 : 2x + y = 5 is a normal to the circle x² + y² – 6x + 2y = 0. 
(a) Statement 1 is false; Statement 2 is true.
(b) Statement 1 is true; Statement 2 is true, Statement 2 is a correct explanation for Statement 1.
(c) Statement 1 is true; Statement 2 is false.
(d) Statement 1 is true; Statement 2 is true; Statement 2 is not a correct explanation for Statement 1.
Answer : A

Question. The set of all real values of λ for which exactly two common tangents can be drawn to the circles
x² + y² – 4x – 4y + 6 = 0 and
x² + y² – 10x – 10y + l = 0 is the interval:
(a) (12, 32)
(b) (18, 42)
(c) (12, 24)
(d) (18, 48)
Answer : B

Question. The circle passing through (1, –2) and touching the axis of x at (3, 0) also passes through the point 
(a) (–5, 2)
(b) (2, –5)
(c) (5, –2)
(d) (–2, 5)
Answer : C

Question. If the circle x² + y² – 6x – 8y + (25 – a²) = 0 touches the axis of x, then a equals.
(a) 0
(b) ±4
(c) ±2
(d) ±3
Answer : B

Question. If each of the lines 5x + 8y = 13 and 4x – y = 3 contains a diameter of the circle x² + y² – 2(a² – 7a + 11) x – 2 (a² – 6a + 6) y + b³ + 1 = 0, then 
(a) a = 5 and b ∉ (-1,1)
(b) a = 1 and b ∉ (-1,1)
(c) a = 2 and b ∉ (-∞,1)
(d) a = 5 and b ∈ (-∞,1)
Answer : D

Question. The equation of the circle passing through the point (1, 2) and through the points of intersection of x² + y² – 4x – 6y – 21 = 0 and 3x + 4y + 5 = 0 is given by
(a) x² + y² + 2x + 2y + 11 = 0
(b) x² + y²– 2x + 2y – 7 = 0
(c) x² + y² + 2x – 2y – 3 = 0
(d) x² + y² + 2x + 2y – 11 = 0
Answer : D

Question. The equation of the circle passing through the point (1, 0) and (0, 1) and having the smallest radius is -
(a) x² + y² - 2x - 2y +1 = 0
(b) x² + y² – x – y = 0
(c) x² + y² + 2x + 2y – 7= 0
(d) x² + y² + x + y – 2 = 0
Answer : B

Question. Three distinct points A, B and C are given in the 2-dimensional coordinates plane such that the ratio of the distance of any one of them from the point (1, 0) to the distance from the point (–1, 0) is equal to 1/3. Then the circumcentre of the triangle ABC is at the point:
(a) (5/4, 0)
(b) (5/2, 0)
(c) (5/3, 0)
(d) (3, 0)
Answer : A

Question. If a circle C passing through (4, 0) touches the circle x² + y² + 4x – 6y – 12 = 0 externally at a point (1, –1), then the radius of the circle C is : 
(a) 5
(b) 2√5
(c) 4
(d) √57
Answer : A

Click on link below to download CBSE Class 11 Conic Section Worksheet A.