Refer to JEE Mathematics Circles MCQs Set C provided below. JEE (Main) 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, JEE (Main) books and examination pattern suggested in Full Syllabus by JEE (Main), NCERT and KVS. Multiple Choice Questions for Circles 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 JEE (Main) Full Syllabus Mathematics and also download more latest study material for all subjects
MCQ for Full Syllabus Mathematics Circles
Full Syllabus Mathematics students should refer to the following multiple-choice questions with answers for Circles in Full Syllabus. These MCQ questions with answers for Full Syllabus Mathematics will come in exams and help you to score good marks
Circles MCQ Questions Full Syllabus Mathematics with Answers
Question: Equation of the circle passing through the origin and through the points of intersection of the circle
x2 + y2– 2x + 4y – 20 = 0 and the line x + y – 1 = 0 is
- a) x2 + y2 – 22x –16y = 0
- b) x2 + y2 - 20x +15y = 0
- c) x2 + y2 + 33x + 33y = 0
- d) None of these
Answer: x2 + y2 – 22x –16y = 0
Question: Equation of the circle concentric with the circle x2 + y2 – 3x+ 4y – c = 0 and passing through the point (–1, – 2).
- a) x2 + y2 - 3x + 4y = 0
- b) x2 + y2 – 7x + 7y = 0
- c) x2 + y2 - 3x - 4y = 0
- d) x2 + y2 + 3x + 4y = 0
Answer: x2 + y2 - 3x + 4y = 0
Question: The straight line (x – 2) + (y + 3) = 0 cuts the circle (x – 2)2 + ( y – 3)2 = 11 at
- a) No points
- b) Two points
- c) One point
- d) None of these
Answer: No points
Question: If the centre of a circle which passing through the points of intersection of the circle x2 + y2 – 6x + 2y + 4 = 0 and x2 + y2 + 2x – 4y – 6 = 0 is on the line y = x, then the equation of the circle is
- a) 7x2 + 7y2 -10x -10y -12 = 0
- b) x2 + y2 + 2x + 4y = 0
- c) 5x2 + 5y2 -10x -10y = 0
- d) 2x2 + 2y2 -3x -3y = 0
Answer: 7x2 + 7y2 -10x -10y -12 = 0
Question: Centre of the circle whose radius is 3 and which touches the circle x2 + y2 – 4x – 6y – 12 = 0 internally at the point (–1, –1) is
- a) (4/7, 7/5)
- b) (5/7, 7/5)
- c) (5/7, 2/5)
- d) none of these
Answer: (4/7, 7/5)
Question: The lines 2x – 3y = 5 and 3x – 4y = 7 are diameters of a circle of area 154 sq.units.Then the equation of the circle is
- a) x2 + y2 - 2x + 2y = 47 .
- b) x2 + y2 + 2x - 2y = 62
- c) x2 + y2 - 2x + 2y = 62
- d) x2 + y2 + 2x - 2y = 47
Answer: x2 + y2 - 2x + 2y = 47 .
Question: If the lines 2x + 3y +1 = 0 and 3x - y - 4 = 0 lie along diameter of a circle of circumference 10p, 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 - 2 y - 23 = 0
- d) x2 + y2 - 2x - 2y - 23 = 0
Answer: x2 + y2 - 2x + 2y - 23 = 0
Question: The point diametrically opposite to the point P(1, 0) on the circle x2 + y2 + 2x + 4y – 3 = 0 is
- a) (–3, –4)
- b) (3, – 4)
- c) (–3, 4)
- d) (3, 4)
Answer: (–3, –4)
Question: The area of a circle centred at (1, 2) and passing through (4, 6) is (in sq. units) is
- a)
- b)
- c)
- d)
Answer:
Question: A circle of radius 5 touches another circle x2 + y2 –2x – 4y –20 = 0 at (5, 5) then its equation is
- a) x2 + y2 – 18x – 16y + 120 = 0
- b) x2 + y2 – 18x + 16y + 120 = 0
- c) x2 + y2 + 18x + 16y + 120 = 0
- d) None of these
Answer: x2 + y2 – 18x – 16y + 120 = 0
Question: The circle x2 + y2 – 8x + 4y + 4 = 0 touches :
- a) y-axis only
- b) None of these
- c) x-axis only
- d) both
Answer: y-axis only
Question: The line 3x – 2y = k meets the circle x2 + y2 = 4r2 at only one point then the value k2 is
- a) 52r2
- b) 32r2
- c) 50 r2
- d) none of these
Answer: 52r2
More Questions..................................
Question: If (– 3, 2) lies on the circle x2 + y2 + 2gx + 2fy + c = 0, which is concentric with the circle x2 + y2 + 6x + 8y – 5 = 0, then c is equal to
- a) – 11
- b) 100
- c) 11
- d) 24
Answer: – 11
Question:
- a) 3/4
- b) 4/3
- c) 1
- d) 12
Answer: 3/4
Question: The length of intercept, the circle
x2 + y2 + 10x – 6y + 9 = 0 makes on the x-axis is :
- a) 8
- b) 4
- c) 2
- d) 6
Answer: 8
Question: If (xi, 1/xi =1, 2, 3, 4 are four distinct points on a circle, then the value of x1 . x2 . x3 . x4 is :
- a) 1
- b) 4
- c) – 1
- d) 0
Answer: 1
Question: If the line x + 2by + 7 = 0 is a diameter of the circle x2 + y2 – 6x + 2y =0, then b =
- a) 5
- b) –5
- c) 3
- d) –1
Answer: 5
Question: If the circle x2 + y2 + 2gx + 2fy + c = 0 touches x-axis, then
- a) g2 = c
- b) g2 + f2 = c
- c) g = f
- d) f2 = c
Answer: g2 = c
Question: The circle x2 + y2 + 4x – 4y + 4 = 0 touches
- a) x-axis and y-axis
- b) x-axis
- c) y-axis
- d) None of these
Answer: x-axis and y-axis
Question:
- a) (2, – 1)
- b) (– 1, 2)
- c) (3, 3)
- d) (– 2, 1)
Answer: (2, – 1)
Question: If a circle S(x, y) = 0 touches the line x + y = 5 at the point (2, 3) and S (1, 2)= 0, then radius of such circle is
- a) 1/√2
- b) 4 units
- c) 2 units
- d) 1/2 units
Answer: 1/√2
Question: In the figure OABC is a square of side 8 cm, then the equation of the smallest circle is
- a) None of these
- b) (x - 4)2 + (y - 4)2 =12
- c) (x - 4)2 + (y - 4)2 = 8
- d) (x - 4)2 + (y - 4)2 = 4
Answer: None of these
Question:
- a)
- b)
- c)
- d)
Answer:
Question:
- a) 1 and 2 are correct
- b) 1 and 3 are correct
- c) 1, 2 and 3 are correct
- d) 2 and 4 are correct
Answer: 1 and 2 are correct
Question: If (a , 0) is a point on a diameter of circle x2 + y2 = 4, then x2 – 4x – a2 = 0 has
(1) exactly one real root in (– 1,0] greater than – 1
(2) exactly one real root in [2, 5] greater than –1
(3) two distinct roots greater than – 1
(4) two distinct root greater than 5
- a) 1, 2 and 3 are correct
- b) 2 and 4 are correct
- c) 1 and 2 are correct
- d) 1 and 3 are correct
Answer: 1, 2 and 3 are correct
Question: One diagonal of a square is the portion of x-axis intercepted by the circle x2 + y2 – 4x + 6y – 12 = 0. Then the y-coordinate of the extrimity above the x-axis of the other diagonal is
(1) ( 2, 4 ) (2) (2, – 4)
(3) (– 2, – 4) (4) (–2, 4)
- a) 1 and 2 are correct
- b) 1 and 3 are correct
- c) 1, 2 and 3 are correct
- d) 2 and 4 are correct
Answer: 1 and 2 are correct
Question: Statement-1 : Number of circles passing through (1, 4), (2, 3), (– 1, 6) is one. Statement-2 : Through 3 non collinear points in a plane only one circle can be drawn.
- a) Statement -1 is False, Statement-2 is True
- b) Statement -1 is True, Statement-2 is False.
- c) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1.
- d) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.
Answer: Statement -1 is False, Statement-2 is True
Question:
Statement-1 : The circle x2 + y2 + 2ax + c = 0 , x2 + y2 + 2by + c = 0 touches each other if 1/a2 + 1/b2 = 1/c
Statement-2 : Two circles with centre C1,C2 and radii r1, r2 touch each other, if r1 ± r2 = C1C2
- a) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.
- b) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1.
- c) Statement -1 is False, Statement-2 is True.
- d) Statement -1 is True, Statement-2 is False.
Answer: Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.
Question: The equation of pair of tangents drawn from the point (0,1) to the circle x2 + y2 – 2x + 4y = 0 is –
- a) 4x2 – 4y2 + 6xy – 6x + 8y –4 = 0
- b) x2 – y2 + 3xy – 3x + 2y –1 = 0
- c) x2 – y2 + 6xy – 6x + 8y –4 = 0
- d) 4x2 – 4y2 + 6xy + 6x + 8y –4 = 0
Answer: 4x2 – 4y2 + 6xy – 6x + 8y –4 = 0
Question: Chord of contact with respect to point (2, 2) of circle x2 + y2 = 1 is -
- a) x + y = 1/2
- b) x + y + 1
- c) x – y = 1/2
- d) x + y = 2
Answer: x + y = 1/2
Question: Distance between the chord of contact with respect to point (0, 0) and (g, f) of circle x2 + y2 + 2gx + 2fy + c = 0 is
- a)
- b)
- c) 1/2 (g2 + f2 + c)
- d) g2 + f2
Answer:
Question: The locus of the centre of the circle which touches externally the circle x2 + y2 – 6x – 6y + 14 = 0 and also touches the y-axis, is -
- a) y2 – 10x – 6y + 14 = 0
- b) x2 – 6x – 10y + 14 = 0
- c) y2 – 6x – 10y + 14 = 0
- d) x2 – 10x – 6y + 14 = 0
Answer: y2 – 10x – 6y + 14 = 0
Question: The two circles x2 + y2 = ax and x2 + y2 = c2 (with c > 0) touch each other if -
- a) c = |a|
- b) 2a = |c|
- c) 2c = a
- d) None of these
Answer: c = |a|
Question: The equation of chord of the circle x2 + y2 = 8x bisected at the point (4, 3) is
- a) y = 3
- b) None
- c) 3y = 1
- d) 4x – 3y = 9
Answer: y = 3
Question: If lines y = x + 3 cuts the circle x2 + y2 = a2 in two points A and B, then equation of circle with AB as diameter is -
- a) x2 + y2 + 3x – 3y – a2 + 9 = 0
- b) x2 + y2 + 3x – 3y + a2 + 9 = 0
- c) x2 + y2 – 3x + 3y – a2 + 9 = 0
- d) None of these
Answer: x2 + y2 + 3x – 3y – a2 + 9 = 0
Question: The equation of the circle which passes through points of intersection of circle x2 + y2 + 4x – 5y + 3 = 0 and x2 + y2 + 2x + 3y – 3 = 0 and point (–3, 2) is -
- a)
- b)
- c) x2 + y2 – 13x + 8y + 3 = 0
- d) x2 + y2 + 8x + 13y – 3 = 0
Answer:
Question: If the circle x2 + y2 + 4x + 22y + c = 0 bisects the circumference of the circle x2 + y2 – 2x + 8y – d = 0, then c + d =
- a) 50
- b) 56
- c) 40
- d) 60
Answer: 50
Question: For what value of k the circles x2 + y2 + 5x + 3y + 7 = 0 and x2 + y2 – 8x + 6y + k = 0 cuts orthogonally ?
- a) –18
- b) 4
- c) 18
- d) – 4
Answer: –18
Question: Equation of polar of point (4, 4) with respect to circle (x –1)2 + (y – 2)2 = 1 is
- a) 3x + 2y – 8 = 0
- b) 3x + 2y + 8 = 0
- c) 2x + 3y – 8 = 0
- d) 3x – 2y + 8 = 0
Answer: 3x + 2y – 8 = 0
Question: The pole of the line x/a + y/b = 1 with respect to circle x2 + y2 = c2 is
- a) (c2/a, c2b)
- b) (c2/a2, c2b2)
- c) (c/a, c/b)
- d) None of these
Answer: (c2/a, c2b)
Question: The radical centre of the three circles
x2 + y2 = a2,(x – c)2 + y2 = a2 and x2 + (y – b)2 = a2 is -
- a) (c/2, b/2)
- b) (a/2, b/2)
- c) (b/2, c/2)
- d) None of these
Answer: (c/2, b/2)
Question: The equation of the radical axis of two circles
x2 + y2 – x + 1 = 0 and 3(x2 + y2) + y – 1 = 0 is -
- a) 3x + y – 4 = 0
- b) 3x – y + 4 = 0
- c) 3x – y – 4 = 0
- d) None of these
Answer: 3x + y – 4 = 0
Question: The locus of the point, the chord of contact of tangents from which to the circle x2 + y2 = a2 subtends a right angle at the centre is a circle of radius -
- a) √2a
- b) 2a
- c) a/2
- d) a2
Answer: √2a
Question: If a chord of the circle x2 + y2 = 8 makes equal intercepts of length a on the coordinate axes, then-
- a) | a | < 4
- b) | a | < 8
- c) | a | > 4
- d) None of these
Answer: | a | < 4
Question: The equation of a normal to the circle
x2 + y2 + 6x + 8y + 1 = 0 passing through (0, 0) is -
- a) 4x – 3y = 0
- b) 3x – 4y = 0
- c) 3x + 4y = 0
- d) 4x + 3y = 0
Answer: 4x – 3y = 0
Question: If the tangent to a circle x2 + y2 = 5 at point (1, –2) touches the circle x2 +y2 – 8x +6y+ 20 = 0, then its point of contact is-
- a) (3, –1)
- b) (5, 0)
- c) (–2, 1)
- d) (–1, –3)
Answer: (3, –1)
Question: Length of the tangent drawn from point (1, 5) to the circle
2x2 + 2y2 = 3 is -
- a) 7 √2 / 2
- b) 7
- c) 7 √2
- d) None of these
Answer: 7 √2 / 2
Question: The area of the triangle formed by the tangents from an external point (h, k) to the circle x2 + y2 = a2 and the chord of contact, is -
- a) a(h2 + k2 - a2 ) 3/2
- b)
- c) None of these
- d)
Answer:
a(h2 + k2 - a2 ) 3/2
Question: The pole of the straight line 9x + y – 28 = 0 with respect to the circle 2x2 + 2y2 – 3x + 5y – 7 = 0, is
- a) (3,–1)
- b) (2, – 1)
- c) (2, 1)
- d) (3,1)
Answer: (3,–1)
Question: The equations of the tangents drawn from the origin to the circle x2 + y2 – 2rx – 2hy + h2 = 0, are
(1) x = 0
(2) y = 0
(3) (h2 – r2)x – 2rhy = 0
(4) (h2 – r2)x + 2rhy = 0
- a) 1 and 3 are correct
- b) 1 and 2 are correct
- c) 1, 2 and 3 are correct
- d) 2 and 4 are correct
Answer: 1 and 3 are correct
Question: Consider the circle x2 + y2 – 10x – 6y + 30 = 0. Let O be the centre of the circle and tangent at A (7, 3) and B (5, 1) meet at C. Let S = 0 represents family of circles passings through A and B, then –
(1) Area of quadrilateral OACB = 4
(2) The smallest possible circle of the family of circles S = 0 is x2 + y2 – 12x – 4y + 38 = 0
(3) The coordinates of point C are (7, 1)
(4) The radical axis for the family of circles S = 0 is x + y = 10
- a) 1, 2 and 3 are correct
- b) 2 and 4 are correct
- c) 1 and 2 are correct
- d) 1 and 3 are correct
Answer: 1, 2 and 3 are correct
Question: A circle x2 + y2 = 1 cuts the line x + y = k and makes the chord with length l. The value of k is –
1. √6/2
2. -√6/2
3. √3/2
4. None of these
- a) 1 and 2 are correct
- b) 1 and 3 are correct
- c) 1, 2 and 3 are correct
- d) 2 and 4 are correct
Answer: 1 and 2 are correct
Question:
Statement-1 : Number of common tangents of x2 + y2 – 2x – 4y – 95 = 0 and x2 + y2 – 6x – 8y + 16 = 0 is zero.
Statement 2 : If C1C2 < | r1 – r2 |, then there will be no common tangent. (where C1, C2 are the centre and r1, r2 are radii of circles).
- a) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.
- b) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1.
- c) Statement-1 is False, Statement-2 is True.
- d) Statement-1 is True, Statement-2 is False.
Answer: Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.
Question:
Statement-1 : The product of slopes of all the common tangents of circles S1 = x2 + y2 – a2 = 0 and S2 = (x – 2a)2 + (y – 2a)2 – 4a2 = 0 is 1.
Statement-2 : Slope of line joining centres of S1 = x2 + y2 – a2 = 0 and S2 = (x – 2a)2 + (y – 2a)2 – 4a2 = 0 is 1. Direct common tangents make equal angles with the line joining centres of the circles.
- a) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.
- b) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1.
- c) Statement-1 is False, Statement-2 is True.
- d) Statement-1 is True, Statement-2 is False.
Answer: Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.
Question:
- a) Statement-1 is False, Statement-2 is True.
- b) Statement-1 is True, Statement-2 is False.
- c) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1.
- d) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.
Answer: Statement-1 is False, Statement-2 is True.
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