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ECAT Pre General Science Mathematics Chapter 23 Conic Section Online Test MCQs With Answers
Question # 1
Choose an answer
none of these
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Question # 2
The equation x
2
+ y
2
= 0 represents
Choose an answer
A circle
A degenerate circle
An empty set
A st. line
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Question # 3
The equation of the normal to the circle x
2
+ y
2
= 25 at (4, 3) is
Choose an answer
3x - 4y =0
3x - 4y =5
4x + 3y = 5
4x + 3y = 25
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Question # 4
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Question # 5
Two circles are said to be concentric if they have
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same radius
same chord
same centre
same diameter
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Question # 6
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Question # 7
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(-6,4)
(-3,2)
(6,-4)
(3, -2)
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Question # 8
If eccentricity of ellipse becomes zero then it takes the form of
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A parabola
A circle
A straight line
None of these
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Question # 9
The two different parts of the hyperbola are called its
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Vertices
Directrices
Nappes
Branches
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Question # 10
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5
25
3
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Question # 11
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Question # 12
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none of these
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Question # 13
A rectangular hyperbola whose centre is C is cut by any circle of radius r in four points P, Q, R and S. Then CP
2
+ CQ
2
+ CR
2
+ CS
2
=
Choose an answer
r
2
2 r
2
3 r
2
4 r
2
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Question # 14
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 # 15
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Question # 16
The lotus of intersection of perpendicular tangents to the parabola y
2
= 4ax is:
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Axis of the parabola
Focal chord of the parabos
The tangent at vertex of the parabola
a directrix of the parabola
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Question # 17
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Question # 18
The length of the tangent from (2, 1) to the circle x
2
+ y
2
+ 4y + 3 = 0 is
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Question # 19
Ifᵨ> 1 , then the conic, is:
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Ellipse
Parabola
Hyperbola
None of these
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Question # 20
The centre of the circle x2+y2 -2fx-2gy+x=0 is
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(-g,-f)
(g,f)
(f,g)
(-f,-g)
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Question # 21
If the cutting plane is parallel to the axis of the cone and intersects both of its nappes, then the curve of intersection is
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an ellipse
a hyperbola
a circle
a parabola
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Question # 22
a chord passing through the focus of a parabola is called a:
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Focal chord
Latus rectum
Tangent
Directrix
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Question # 23
ax2 +2hxy +by2 +2gx +2fy +c =0 may represent an ellipse if
Choose an answer
h2 -ab <0
h2 -ab≠ 0
h2 -ab =0
h2 -ab >0
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Question # 24
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2 b
2 a
2 ab
a + b
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Question # 25
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none of these
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Question # 26
The equation of the chord of the circle x
2
+ y
2
- 4x = 0 whose mid-point is (1, 0) is
Choose an answer
y = 2
y = 1
x = 2
x = 1
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Question # 27
If the focus lies on the y-axis with coordinates f(0,a) and directrix of the parabola is y = -a, the equation of parabola is:
Choose an answer
y
2
= -4 ax
x
2
= 4ay
x
2
= -4ay
y
2
= 4ax
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Question # 28
The eccentricity of the parabola y
2
= -8x is
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-2
2
-1
1
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Question # 29
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none of these
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Question # 30
For what value of k, 3x -2y+ k= 0 is tangent to the circle x2 +y2 +6x -4y =0
Choose an answer
k=0
k=0 or 26
k = 26
k=-13
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Question # 31
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none of these
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