CBSE Class 11 Mathematics Conic Sections Assignment Set 01

Question. If a circle passes through the point (a, b) and cuts the circle x² + y² = p orthogonally, then the equation of the locus of its centre is
(a) x² + y² – 3ax – 4by + (a² + b² - p²) = 0
(b) 2ax + 2by – (a² - b² + p²) = 0
(c) x² + y² – 2ax – 3by + (a² - b² - p² ) = 0
(d) 2ax + 2by – (a² + b² + p² ) = 0
Answer : D

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

Question. The two circles x² + y² = ax and x² + y² = c² (c > 0) touch each other if
(a) | a | = c
(b) a = 2c
(c) | a | = 2c
(d) 2 | a | = c
Answer : A

Question. The length of the diameter of the circle which touches the x-axis at the point (1,0) and passes through the point (2,3) is:
(a) 10/3
(b) 3/5
(c) 6/5
(d) 5/3
Answer : A

Question. The number of common tangents of the circles given by x² + y² – 8x – 2y + 1 = 0 and x² + y² + 6x + 8y = 0 is
(a) one
(b) four
(c) two
(d) three
Answer : C

Question. The circle x² + y² = 4x + 8y + 5 intersects the line 3x – 4y = m at two distinct points if
(a) – 35 < m < 15
(b) 15 < m < 65
(c) 35 < m < 85
(d) – 85 < m < – 35
Answer : A

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 -10ab + 3b² = 0
(b) 3a² - 2ab + 3b² = 0
(c) 3a² +10ab + 3b² = 0
(d) 3a² + 2ab + 3b² = 0
Answer : D

Question. The lines 2x - 3y = 5 and 3x - 4y = 7 are diameters of a circle having area as 154 sq.units.Then the equation of the circle is
(a) x² + y² - 2x + 2y = 62
(b) x² + y² + 2x - 2y = 62
(c) x² + y² + 2x -2 y = 47
(d) x² + y² - 2x + 2y = .47
Answer : D

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 : C

Question. The centre of the circle passing through (0, 0) and (1, 0) and touching the circle x² + y² = 9 is
(a) (1/2, 1/2)
(b) (1/2, - √2)
(c) (3/2, 1/2)
(d) (1/2, 3/2)
Answer : B

Question. If the chord y = mx + 1 of the circle x² + y² = 1 subtends an angle of measure 45 at the ma or segment of the circle then value of m is
(a) 2 ± √2
(b) –2 ± √2
(c) –1 ± √2
(d) none of these
Answer : C

Question. 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 5x + by – a = 0 passes through P and Q for
(a) exactly one value of a
(b) no value of a
(c) infinitely many values of a
(d) exactly two values of a
Answer : B

Question. If a circle passes through the point (a, b) and cuts the circle x² + y² = 4orthogonally, 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
Answer : B

Question. If two vertices of an equilateral triangle are A (– a, 0) and B (a, 0), a > 0, and the third vertex C lies above x-axis then the equation of the circumcircle of ΔABC is :
(a) 3x² + 3y² – 2√3ay = 3a²
(b) 3x² + 3y² - 2ay = 3a²
(c) x² + y² - 2ay = a²
(d) x² + y² - √3ay = a²
Answer : A

Question. If P and Q are the points of intersection of the circles x² + y²+ 3x + 7y + 2p - 5 = 0 and x² + y² + 2x + 2y – p² = 0 then there is a circle passing through P, Q and (1, 1) for: 
(a) all except one value of p
(b) all except two values of p
(c) exactly one value of p
(d) all values of p
Answer : A

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) (y - q)² = 4px
(b) (x - q)² = 4 py
(c) (y - p)² = 4qx
(d) (x - p)² = 4qy
Answer : D

Question. Let C be the circle with centre (0, 0) and radius 3 units. The equation of the locus of the mid points of the chords of the circle C that subtend an angle of 2π/3 at its center is
(a) x² + y² = 3/2
(b) x² + y² = 1
(c) x² + y² = 27/4
(d) x² + y² = 9/4
Answer : D

Question. 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 - y = 0
(b) x² + y² - x + y = 0
(c) x² + y² + x + y = 0
(d) x² + y² - x - y = 0
Answer : D

Question. If the two circles (x -1)² + ( y - 3)² = r² and x² + y² - 8x + 2y + = 0 intersect in two distinct point, then
(a) r > 2
(b) 2 < r < 8
(c) r < 2
(d) r = 2.
Answer : B

Question. The centres of a set of circles, each of radius 3, lie on the circle x² + y²=25. The locus of any point in the set is
(a) 4 ≤ x² + y² ≤ 64
(b) x² + y² ≤ 25
(c) x² + y² ³ 25
(d) 3 ≤ x² + y² ≤ 9
Answer : A

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 + 2y - 23 = 0
(d) x² + y² - 2x + 2y - 23 = 0
Answer : D

Question. The equation of a circle with origin as a centre and passing through equilateral triangle whose median is of length 3a is
(a) x² + y² = 9a²
(b) x² + y² = 16a²
(c) x² + y² = 4a²
(d) x² + y² = a²
Answer : C