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ECAT Pre General Science Mathematics Chapter 23 Conic Section Online Test MCQs With Answers
Question # 1
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 # 2
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Question # 3
The point on y
2
= 4ax nearest to the focus has its abciassae equal to
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-a
a
a/2
0
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Question # 4
If (0, 0) and (0, -1) are end points of a diameter, then the equation of the circle is
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Question # 5
If the cutting plane is slightly tilted and cuts only one nappe of the cone, the intersection is
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an ellipse
a hyperbola
a circle
a parabola
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Question # 6
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(g,f)
(-g,f)
(g,-f)
(-g,-f)
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Question # 7
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 # 8
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c = 0
c = -1
c = -2
c = 1
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Question # 9
The vertices of the ellipse x
2
+ 4y
2
= 16 are
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Question # 10
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 # 11
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An ellipse
A parabola
A circle
A hyperbola
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Question # 12
Equation of parabola with focus F(-3,1) directrix x=3 is
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(y -1)2 =-12x
(y-1)2 =4x
(x+3)2 =4a(y-1)
y2 =-12(x-1)
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Question # 13
ax2 +2hxy +by2 +2gx +2fy +c =0 may represent an ellipse if
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h2 -ab <0
h2 -ab≠ 0
h2 -ab =0
h2 -ab >0
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Question # 14
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Question # 15
the latus rectum of the parabola x
3
= -4ay is:
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x = a
y = -a
x = -a
y = 0
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Question # 16
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8
4
64
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Question # 17
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 # 18
If x + y + 1 = 0 touches the parabola y
2
=
λ
x, then
λ
is equal to
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2
4
6
8
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Question # 19
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6
20
0
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Question # 20
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none of these
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Question # 21
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Question # 22
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 # 23
The perpendicular bisector of any chord of a circle
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Passes through the centre of the circle
Does not pass through the centre of the circle
May or may not pass through the centre of the circle
None of these
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Question # 24
The parabolay2=4ax open up if
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a<0
a≠0
a>0
All are incorrect
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Question # 25
The equation of the tangent at vertex to the parabola is y2 = -8(x -3)
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y=0
x=3
x=1
x=5
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Question # 26
If the st. line 3x + 4y = K touches the circle x
2
+ y
2
- 10x = 0 then the value of K is
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-1 or 20
-10 or 40
-2 or 20
2 or 20
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Question # 27
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(1, 3)
(-1, -3)
(1, -3)
(-1, 3)
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Question # 28
A line joining two distinct points on a parabola is called a ______ of the parabola.
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Chord
Tangent
Lust rectum
directrix
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Question # 29
Intersection of two parabolas
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parabola
Two points
Four points
Hyperobla
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Question # 30
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 # 31
A line joining two distinct points on a parabola is called
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Axis
Directrix
Chord
Tangent
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