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ECAT Pre General Science Mathematics Chapter 23 Conic Section Online Test MCQs With Answers
Question # 1
If (x
1
, y
1
) and (x
2
,
y
2
) are the end points of a diameter then the centre of the circle is
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Question # 2
The slope of the normal at the point (at
2
, 2at) of the parabola y
2
= 4ax is
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1/t
t
-t
-1/t
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Question # 3
If the circle x
2
+ y
2
+ 2gx +2fy + c = 0 passes through the origin then
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c = 0
c = -1
c = -2
c = 1
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Question # 4
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Question # 5
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none of these
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Question # 6
Circumcentre of the triangle, whose vertices are (0, 0), (6, 0) and (0, 4) is
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(2, 0)
(3, 0)
(0, 3)
(3, 2)
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Question # 7
The line through the focus and perpendicular to the directrix is called ______ of the parabola
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axis
focal chord
tangent
latus rectum
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Question # 8
If (0, 0) and (1, 0) are the end points of a diameter, then the equation of the circle is
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Question # 9
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Question # 10
The locus of the point of intersection of tangents to an ellipse at two points, sum of whose eccentric angles is constant is
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A parabola
A circle
An ellipse
A st. line
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Question # 11
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An ellipse
A parabola
A circle
A hyperbola
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Question # 12
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Question # 13
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2 b
2 a
2 ab
a + b
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Question # 14
The centre fo the circle x
2
+ y
2
+ 12x -10 = 0 is
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(12, -10)
(6, -5)
(-12, 10)
(-6, 5)
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Question # 15
Coordinates of the focus of the parabola x
2
- 4x -8y-4=0 are:
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(0,2)
(,0,1)
(2,0)
(1,2)
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Question # 16
If (0, 0) and (-1, 0) are end points of a diameter, then the equation of the circle is
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Question # 17
x =r cosθ,y= sinθ are the parametric equations of
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Circle
Ellipse
Parabola
Hyoerbola
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Question # 18
The common point to four standard parabolas
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Focus
Centre
Vertex
P(x,y)
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Question # 19
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Question # 20
The equation of the circle with centre (-h, -k) and radius r is
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(x +h)
2
+ (y+k)
2
= r
2
(x +h)
2
+ (y-k)
2
= r
2
(x -h)
2
+ (y+k)
2
= r
2
(x -h)
2
+ (y-k)
2
= r
2
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Question # 21
The parabola y
2
= x is symmetric about
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x-axis
y-axis
Both x and y-axis
The line y = x
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Question # 22
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Question # 23
The constant distance of all points of the circle from its centre is called the
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radius of the circle
secant of the circle
chord of the circle
diameter of the circle
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Question # 24
Area of the circle with ends of a diameter at (-3,2) and (5,-6)
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128π sq. units
64π sq. units
32π sq.units
None of these
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Question # 25
The equation of the circle with centre (h, k) and radius r is
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(x+ h)
2
+ (y+ k)
2
= r
2
(x+ h)
2
+ (y - k)
2
= r
2
(x - h)
2
+ (y+ k)
2
= r
2
(x - h)
2
+ (y - k)
2
= r
2
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Question # 26
Co-ordinate of a point on the parabola y
2
= 8x whose focal distance is 4 are:
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(2 , 4)
(-2 ,-4)
(-2, 4)
(2,-4)
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Question # 27
The line y = 2 x + c is a tangent to the parabola y
2
= 16 x if c equals
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-2
-1
0
2
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Question # 28
A line segment whose end points lie on a circle is called
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the secant of the circle
the arc of the circle
the chord of the circle
the circumference of the circle
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Question # 29
A square is inscribed in the circle x
2
+ y
2
- 2x + 4y + 3 =0. Its sides are parallel to the co-ordinate axes. Then one vertex of the square is
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Question # 30
If the intersecting plane is parallel to a generator of the cone, but intersects its one nappe only, the curve obtained is
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an ellipse
a hyperbola
a circle
a parabola
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Question # 31
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none of these
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