Purpose:
1. _Assessment_: To assess the mathematical knowledge and skills of students
2. _Practice_: To provide students with practice questions for improving their mathematical skills
3. _Education_: To educate students on various mathematical concepts and principles
2. The area of triangle formed by the tangent, normal drawn at (1, √3) to the circle x2 + y2 = 4 and the positive x-axis, is
–
– –
a) 5√3 b) 4√3
– –
c) 2√3 d) √3
3. The equation of the circle of radius 5 and touching the coordinate axes in third quadrant, is
j
a) (x + 4)2 + (y + 4)2 = 25 b) (x + 6)2 + (y + 6)2 = 25
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4. Let C be the circle with centre (0, 0) and radius 3 units. The equation of the locus of the mid-point of the chords of the
circle C that subtend an angle of 2π
3
at its centre is
a) x2 + y2 = 9
b) x2 + y2 = 27
4 4
c) x2 + y2 = 1 d) x2 + y2 = 3
2
5. ax2 + 2y2 + 2bxy + 2x - y + c = 0 represents a circle through the origin, if
a) a = 1, b = 2, c = 0 b) a = 0, b = 0, c = 2
c) a = 2, b = 2, c = 0 d) a = 2, b = 0, c = 0
6. If a circle passes through the point (0, 0), (a, 0), (0, b), then its centre is
a) (a, b) b) (
b
,−
a
)
2 2
c) (b, a) d) (
a
,
b
)
2 2
7. The equation of a circle whose diameter is the line joining the points (-4, 3) and (12, -1) is
8. A circle touching the X-axis at (3, 0) and making an intercept of length 8 on the Y-axis passes through the point
a) (2, 3) b) (3, 10)
1/3
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, c) (1, 5) d) (3, 5)
9. The locus of the centres of the circles, which touch the circle, x2 + y2 = 1 externally, also touch the Y-axis and lie in the
first quadrant, is
−−−− − −−−− −
a) x = √1 + 4y , y ≥ 0 b) x = √1 + 2y , y ≥ 0
−−−− − −−−− −
c) y = √1 + 2x , x ≥ 0 d) y = √1 + 4x , x ≥ 0
10. A variable tangent to the circle x2 + y2 = r2 at P cuts the coordinate axes at A and B. The path of midpoint M of AB is
given by
a) 1
x
2
+
1
y
2
= 4r
2
b) r
2
(
1
2
+
1
2
) = 2
x y
2
c) r 2
(
1
+
1
) = 4 d) 1
2
+
1
2
=
r
2
x y
2
x y 4
11. Area of the equilateral triangle inscribed in the circle x2 + y2 - 7x + 9y + 5 = 0 is
– –
a) 175
8
√3 square units b) 185
8
√3 square units
– –
c) square units d) square units
165 155
√3 √3
8 8
12. If the line 2x + 3y = 3 intersects the circle x2 + y2 - 4 = 0 at A and B and M(α, β ) is point of intersection of the tangents
at A and B, then α
β
is equal to:
a) 3
2
b) 2
3
c) 4
d) 3
3 4
j
13. Let L1 be a straight line passing through the origin and L2 be the straight line x + y = 1. If the intercepts made by the
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circle x2 + y2 - x + 3y = 0 on L1 and L2 are equal, then which of the following equations can represent L1?
a) x - 7y = 0 b) x - y = 0, x + 7y = 0
c) 7x + y = 0 d) x + y = 0, x - 7y = 0
14. The equation of the circle whose centre is (3, -1) and which cuts off a chord of length 6 on the line 2x - 5y + 18 = 0 is
15. If the coordinates of one end of the diameter of the circle x2 + y2 - 8x - 4y + c = 0 are (-3, 2), then the coordinates of
other end are
a) (6, 2) b) (5, 3)
c) (1, -8) d) (11, 2)
16. The equation of a circle with origin as centre and passing through the vertices of an equilateral triangle whose median is
of length 3a is
a) x2 + y2 = a2 b) x2 + y2 = 9a2
c) x2 + y2 = 4a2 d) x2 + y2 = 16a2
17. The line lx + my + n = 0 will be a tangent to the circle x2 + y2 = a2 if
a) a2(I2 + m2) = n2 b) n2(l2 + m2) = a2
2/3
***
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