Please refer to Chapter 11 Conic Sections MCQ Class 11 Mathematics with answers below. These multiple-choice questions have been prepared based on the latest NCERT book for Class 11 Mathematics. Students should refer to MCQ Questions for Class 11 Mathematics with Answers to score more marks in Grade 11 Mathematics exams. Students should read the chapter Conic Sections and then attempt the following objective questions.

MCQ Questions Class 11 Mathematics Chapter 11 Conic Sections

The Conic Sections MCQ Class 11 Mathematics provided below covers all important topics given in this chapter. These MCQs will help you to properly prepare for exams.

Question. The tangent drawn at any point P to the parabola y² = 4ax meets the directrix at the point K, then the angle which KP subtends at its focus is
(a) 30°
(b) 45°
(c) 60°
(d) 90°

Question: If the lines 3x-4y-7=0 and 2x-3y-5=0  are two diameters of a circle of area 49π sq units, the equation of the circle is 
(a) x²+ y²+ 2x- 2y- 62=0 
(b) x²+ y²– 2x + 2y- 62=0 
(c) x²+ y² -2x + 2y-47=0 
(d) x²+ y² + 2x- 2y-47=0 

Question: If the pair of lines ax²+ 2(a+b) xy+by²= 0  lie along diameters of a circle and divide the circle into four sectors such that the area of one of the sectors is thrice the area of another sector, then 
(a) 3a²+2ab+3b²=0
(b) 3a²+10ab+3b²=0
(c) 3a²-2ab+3b²=0
(d) 3a²-10ab+3b²=0 

Question:  Let C be the circle with centre (0, 0) and radius 3. The equation of the locus of the mid-points of the chords of the circleC that subtend an angle 2π/3 at its centre is

Question: A circle touches the x-axis and also touches the circle with centre at (0, 3) and radius 2. The locus of the centre of the circle is
(a) a parabola
(b) a hyperbola
(c) a circle
(d) an ellipse

Question: The smallest circle with centre on y-axis and passing through the point (7, 3) has radius 
(a) √58
(b) 7
(c) 3
(d) 4

Question:  If the lines 2x+3y+1=0  and 3x-y-4=0  along diameters of a circle of circumference 10π, then the equation of the circle is 
(a) x² + y² -2x +2y -23=0
(b) x² + y² -2x +2y -23=0
(c) x² + y² -2x +2y -23=0
(d) x² + y² +2x -2y -23=0

Question: The intercept on the line y=x  by the circle x²+y²-2x=0 is AB. Equation of the circle on AB as a diameter is 
(a) x2 +y² – x- y =0
(b) x² +y² – x +y=0 
(c) x² +y² + x +y=0 
(d) x² +y² +x -y=0

Question: If a circle passes through the point(a ,b) and cuts the circle x²+y² = 4 orthogonally, then the locus of its centre is 
(a) 2ax+2by+(a²+b²+4) =0
(b) 2ax+2by+(a²+b²+4) =0
(c) 2ax- 2by+(a²+b²+4) =0
(d) 2ax- 2by- (a²+b²+4) =0

Question:  A variable circle passes through the fixed point A(p, q) and touches x-axis. The locus of the other end of the diameter through A is
(a) (x-p)²=4gy  
(b) (x-q)²=4py) 
(c) (y-p)²=4qx 
(d) (y-q)²=4px

Question: 41. If the circles x²+ y² +2ax +cy +a= 0  and x² +y² -3ax +dy-1=0  intersect in two distinct points P and Q, then the line 5 0 x by a + − = passes through P and Q for
(a) no value of a
(b) exactly one value of a
(c) exactly two values of a
(d) infinitely many values of a

Question:  How many common tangents can be drawn to the following circles x²+y²=  6 and x²+y²+6x+2y+1=0  ? 
(a) 4
(b) 3
(c) 2
(d) 1

Question:  The line 3x-2y=k meets the circle x²+ y²=4r² at only one point, if k²
(a) 20r²  
(b) 52/9 r²
(c) 52/9^r2 
(d) 20/9r²

Question:  If the line 3x-4y-k=0,(k>0) touches the circle x²+y²-4x-8y-5=0 at (a ,b ) then k+ a+ b is equal to
(a) 20
(b) 22
(c) −30
(d) −28 

Question:  Find the equation of the circle which passes through the points (2, 3) and (4, 5) and the centre lies on the straight line y-4X+3=0 .
(a) x²+ y² – 4x – 10y +25= 0
(b) x² +y² -4x -10y – 25= 0
(c) x² +y² -4x+ 10y -25= 0
(d) None of the above 

Question:  If the line x /a+y/ b=1 moves such that 1/a²+1/b²=1/c²‘ where c is a constant, then the locus of the foot of the perpendicular from the origin to the line is
(a) straight line
(b) circle
(c) parabola
(d) ellipse

Question:  A line through P(1 , 4) intersect a circle x²+y²=16 at A B and , then A and B,then pA·PB is equal to
(a) 1
(b) 2
(c) 3
(d) 4 

Question:  A line through (0, 0) cuts the circle x²+y²-2ax=0  at A B and , then locus of the centre of the circle drawn AB as diameter is
(a) x²+ y²– 2ay =0
(b) x²+y²+ay=0
(c) x²+ y²+ ax =0
(d) x²+y²-ax=0 

Question:  The equation of the tangents to the circle x2+y2=4,which are parallel to x y + + = 2 3 0, are
(a) x-2y=2
(b) x +2y= ±2√3
(c) x+2y= ± 2 √5
(d) x- 2y = ± 2√5 

Question: 

Question:  If a circle passes through the point of intersection of the coordinate axes with the lines λx-y +1=0 and x -2y + 3 0, then the value of λ is
(a) 2
(b) 4
(c) 6
(d) 3 

Question:  The square of the length of the tangent from (3,-4) to the circle x²+y²-4x-6y+3=0  is
(a) 20
(b) 30
(c) 40
(d) 50 

Question: The length of the tangent drawn from any point on

Question:  The tangent at (1,7) to the curve x²= y- 6  touches the circle x²+y²+16x+12y+c=0 at
(a) (6, 7)
(b) (- 6,7 ) 
(c) ( 6,7)
(d) (-6,7)   

Question: The normal at the point (3, 4) on a circle cuts the circle at the point (–1, –2). Then, the equation of the circle is
(a) x²+ y²+ 2x-2y -13 =0
(b) x² +y²– 2x-2y -11 =0
(c) x²+ y² -2x +2y +12 =0
(d) x² +y² -2x -2y +14 =0 

Question:  Centre of circle whose normals are x²-2xy-3x+6y=0  is
 (a) (3,3/2)
 (b) (3,3/2)
 (c) (3/2,3)
 (d) None of these 

Question: If line ax by + = 0 touches x²+y²+2x+4y=0  and is a normal to the circle x²+y²-4x+2y-3=0, then value of (a ,b ) will be
(a) (2,1)
(b) (1, –2)
(c) (1, 2)
(d) (–1, 2) 

Question. If the tangents at P and Q on the parabola meet in T, then SP, ST and SQ are in
(a) AP
(b) GP
(c) HP
(d) None of these

Question. AB, AC are tangents to a parabola y² = 4ax; p₁ ,p₂ , p3 are the lengths of the perpendiculars from A, B,C on any tangent to the curve, then p1 ,p2 , p3 are in
(a) AP
(b) GP
(c) HP
(d) None of these

Question. The length of the chord of the parabola y² = x which is bisected at the point (2, 1) is
(a) 2√3
(b) 4√3
(c) 3√2
(d) 2√5

Question. The DPQR of area A is inscribed in the parabola y² = 4ax such that the vertex P lies at the vertex of the parabola and the base QR is a focal chord. The modules of the difference of the ordinates of the points Q and R is
(a) A/2a
(b) A/a
(c) 2A/a
(d) 4A/a

Question. On the parabola y = x², the point atleast distance from the straight line y = 2x – 4 is
(a) (1, 1)
(b) (1, 0)
(c) (1, -1)
(d) (0, 0)

Question. If the equation of parabola is x² = – 9y , then equation of directrix and length of latusrectum are
(a) y = -9/4 ,8
(b) x = 9/4 ,9
(c) y = -9/4 ,8
(d) None of these

Question. Consider the following statements
I. The equation of the parabola whose focus is at the origin is y² = 4ax.
II. The line lx + my + n = 0 will touch the parabola
y² = 4ax , if ln = am².
Which of these is/are correct ?
(a) Only (I)
(b) Only (II)
(c) Both of these
(d) None of these

Question. The number of distinct normals that can be drawn to parabola  y² = 16x from the point (2, 0), is
(a) 1
(b) 2
(c) 3
(d) 0

Question. The length of the chord of the parabola x² = 4y passing through the vertex and having slope cota is
(a) 4 cosa cosec²a
(b) 4 tana sec a
(c) 4 sin a sec²a
(d) None of these 

Question. If the vertex of the parabola is the point (– 3, 0) and the directrix is the line x + 5 = 0, then its equation is 
(a) y² = 8(x+ 3)
(b) x² = 8(y+ 3)
(c) y²  = – 8(x+ 3)
(d) y² = 8(x+ 5)

Question. The arithmetic mean of the ordinates of the feet of the normals from (3, 5) to the parabola y² = 8x is 
(a) 4
(b) 0
(c) 8
(d) None of these

Question. The line x – 1 = 0 is the directrix of the parabola y² – kx  + 8 = 0. Then, one of the value of k is
(a) 1/8
(b) 8
(c) 4
(d) 1/4

Question. If the focus of a parabola is (0, – 3) and its directrix is y = 3 and its equation is
(a) x² = – 12y
(b) x² = 12y
(c) y²   = – 12x
(d) y²= 12x

Question. If two different tangents of y² = 4ax are the normals to x² = 4by , then
(a) |b|>1/2√2
(b) |b|<1/2√2
(c) |b |> 1/√2
(d) |b |< 1/√2

Question. Equation of chord of the parabola y² = 16 whose mid-point is (1, 1), is
(a) x + y = 2
(b) x – y = 0
(c) 8x + y = 9
(d) 8x – y = 7

Question. The chord AB of the parabola y² = 4ax cuts the axis of the parabola at C. If A = (at₁² , 2at₁ )  B = (at₂² , 2at₂ ) and AC: AB= 1:3, then
(a) t₂ = 2t₁
(b) t₂ + 2t₁ = 0
(c) t₁ + 2t₂ = 0
(d) None of these

Question. AB is a chord of the parabola x² = 4ax with vertex A, BC is drawn perpendicular to ABmeeting the axis atC. The projection of BC on the axis of the parabola is
(a) a
(b) 2a
(c) 4a
(d) 8a

Question. The focal chord to  y² = 16 is tangent to (x – 6)2 + y² = 2  , then the possible values of the slope of this chord are
(a) {-1,1}
(b) {-2,2}
(c) {-2,1/2}
(d) {2,-1/2}

Question. Let P be the point (1, 0) and Q a point on the locus y² = 8x . The locus of mid-point of PQ is
(a) x² – 4y + 2 = 0
(b) x² – 4y + 2 = 0
(c) y² + 4y + 2 = 0
(d) y² – 4y + 2 = 0

Question. If a parabolic reflector is 20 cm in diameter and 5 cm deep, then the focus is 
(a) (0, 5)
(b) (5, 0)
(c) (0, -5)
(d) (-5, 0)

Question. Find the area of the triangle formed by the lines joining the vertex of the parabola x² = 12 to the ends of its latusrectum. 
(a) 19 sq units
(b) 18 sq units
(c) 20 sq units
(d) 17 sq units

Question. Find the length of the line segment joining the vertex of the parabola y² = 4ax and a point on the parabola where the line segment makes an angle q to the x-axis.
(a) 2a cosΘ /sin²Θ
(b) 4a cosΘ /sin²Θ
(c) 4a cosΘ /3sin²Θ
(d) None of these

Question. If a ¹ 0 and the line 2bx + 3cy + 4d = 0 passes through the points of intersection of the parabolas y² = 4ax and x² = 4ay , then
(a) d² + (2b + 3c)² = 0
(b) d² + (3b + 2c)² = 0
(c)  d² + (2b – 3c)² = 0
(d)  d² + (3b+ 2c)² = 0

Question. The circle x² + y²  + 2λx = 0, λ∈R, touches the parabola y² = 4x externally. Then,
(a) λ> 0
(b) λ < 0
(c) λ > 1
(d) None of these

Question. The shortest distance between the parabolas y² = 4x and y² = 6x is
(a) 2
(b) √5
(c) 3
(d) None of these

Question. A parabola is drawn with focus at (3, 4) and vertex at the focus of the parabola y² – 12x – 4y + 4 = 0. The equation of the parabola is
(a) x² – 6x – 8y + 25 = 0
(b) y² – 8x – 6 + 25 = 0
(c) x² – 6x + 8y – 25 = 0
(d) x² – 6x – 8y – 25 = 0

Question. The normal to the parabola y² = 8x at the point (2, 4) meets the parabola again at the point
(a) (-18, -12)
(b) (-18,12)
(c) (18, 12)
(d) (18, -12)

Question. Three distinct normals to the parabola y² = x are drawn through a point (c,0), then
(a) c = 1/4
(b) c = 1/2
(c) c > 1/2
(d) None of these

Question. If y₁ , y₂ , y₃ , and are the ordinates of the vertices of a triangle inscribed in the parabola y² = 4ax , then its area is
(a) 1/2a (y₁ – y₂)(y₂-y₃)(y₃– y₁)
(b) 1/4a (y₁ – y₂)(y₂-y₃)(y₃– y₁)
(c) 1/8a (y₁ – y₂)(y₂-y₃)(y₃– y₁)
(d) None of the above

Question. The locus of a point on the variable parabola y² = 4ax , whose distance from focus is always equal to k, is equal to (a is parameter)
(a) 4x² + y² – 4kx = 0
(b) x² + y² – 4kx = 0
(c) 2x² + 4y² – 8kx = 0
(d) 4x² – y² + 4kx = 0

Question. The radius of circle when a attains its maximum value 
(a) 1/√10
(b) 1/√5
(c) 1
(d) 5

Question. The slope of the tangent when radius of the circle is maximum is
(a) 1
(b) 1
(c) 0
(d) 2

Question. The equation of the parabola whose focus is the point (0, 0) and the tangent at the vertex is x – y + 1 = 0 is
(a) x² + y² – 2xy – 4x – 4y – 4 = 0
(b) x² + y²  – 2xy + 4x – 4y – 4 = 0
(c) x² + y² – 2xy – 4x + 4y – 4 = 0
(d) x² + y² – 2xy – 4x + 4y – 4 = 0

Question. Axis of a parabola is y = x and vertex and focus are at a distance 2 and 2 √2 respectively from the origin. Then, equation of the parabola is
(a) (x – y )² = 8(x + y – 2)
(b) (x – y )² = 2(x + y – 2)
(c) (x – y )2 = 4(x + y – 2)
(d) (x + y )² =2(x – y + 2)

Question. The minimum area bounded by the tangent and the coordinate axes is
(a) 1
(b) 1/3
(c) 1/2
(d) 1/4

Directions (Q. Nos. 14-18) Each of these questions contains two statements : Statement I (Assertion) and Statement II (Reason). Each of these questions also has four alternative choices, only one of which is the correct answer. You have to select one of the codes (a), (b), (c) and (d) given below.
(a) Statement I is true, Statement II is true; Statement II is a correct explanation for Statement I.
(b) Statement I is true, Statement II is true; Statement II is not a correct explanation for Statement I.
(c) Statement I is true; Statement II is false.
(d) Statement I is false; Statement II is true.

Question. Statement I If normal at the ends of double ordinate x = 4 of parabola y² = 4x meet the curve again at P and P¢ respectively, then PP’ = 12 units.   
Statement II If normal at t1 of y ax 2 = 4 meet the parabola again at t2, then t2 = t1 -2/t1

Question. Statement I The lines from the vertex to the two extremities of a focal chord of the parabola y2 = 4ax are at an angle of π/2

Statement II If extremities of focal chord of parabola are (at12 ,2at1 ) and (at22 , 2at2) , then t1t2 = – 1.

Question. Statement I The latusrectum of a parabola is 4 units, axis is the line 3x + 4 y – 4 = 0 and the tangent at the vertex is the line 4x – 3 y + 7 = 0, then the equation of directrix of the parabola is 4x – 3 y + 8 = 0.    

Statement II If P be any point on the parabola and let PM and PN are perpendiculars from P on the axis and tangent at the vertex respectively, then (PM)2 = (latusrectum) (PN)

Question. Statement I Slope of tangents drawn from (4, 10) to parabola y² = 9x are 1/4,9/4     
Statement II Two tangents can be drawn to parabola from any point lying outside parabola. 

Question. Statement I In parabola y ax 2 = 4 , the circle drawn taking focal radii as diameter touches y-axis.
Statement II The portion of the tangent intercepted between point of contact and directrix subtends 90° angle at focus.     

Question. If two tangents drawn from a point P to the parabola y² = 9x are at right angles, then the locus of P is
(a) x = 1
(b) 2x + 1 = 0
(c) x = -1
(d) 2x – 1 = 0 

Question. A parabola has the origin as its focus and the line x = 2 as the directrix. Then, the vertex of the parabola is at
(a) (2, 0)
(b) (0, 2)
(c) (1, 0)
(d) (0, 1)

Question. The equation of the tangent to the parabola y² = 8x is y = x + 2. The point on this line from which the other tangent to the parabola is perpendicular to the given tangent is 
(a) (0, 2)
(b) (2, 4)
(c) (-2, 0)
(d) (-1, 1)

Question. Let P be a point whose coordinates differ by unity and the point does not lie on any of the axes of reference. If the parabola y² = 4x + 1 passes through P, then the ordinate of P may be
(a) 3
(b) -1
(c) 5 
(d) 1

Question. Parabola y2 = 4x and the circle having it’s centre at (6, 5) intersect at right angle. Possible point of intersection of these curves can be
(a) (9, 6)
(b) (2,√8)
(c) (4, 4)
(d) (3, 2√3)   

Question. If the normals at two points P and Q of a parabola y² = 4ax intersect at a third point R on the curve, then the product of ordinates of P and Q is
(a) 4a²
(b) 2a²
(c) – 4a²
(d) 8a²

Question. If the tangent and normal at any point P of a parabola meet the axes in T andG respectively, then
(a) ST ¹ SG = SP
(b) ST – SG ¹ SP
(c) ST = SG = SP
(d) ST = SG × SP

Question. The locus of the vertices of the family of parabolas y = a² x² /3 + a² x/2 – 2a is
(a) xy = 35/36
(b) xy = 64/105
(c) xy = 105/64
(d) xy = 3/4

Question. If tangents at A and B on the parabola y² = 4 intersect at pointC, then ordinates of A,C and Bare
(a) always in AP
(b) always in GP
(c) always in HP
(d) None of these

Question. The number of real tangents that can be drawn to the curve y² + 2xy + x² + 3y + 1 = 0 from the point (1, – 2) is
(a) one
(b) two
(c) zero
(d) None of these

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