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Online Tests
ECAT Pre General Science Mathematics Chapter 23 Conic Section Online Test MCQs With Answers
Question # 1
The tangents drawn from the point P to a circle are real and coincident if
Choose an answer
P is on the circle
P is inside the circle
P is outside the circle
none of these
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Question # 2
The line 3x - 4y = 0
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Is a tangent to the circle x
2
+ y
2
= 25
Is a normal to the circle x
2
+ y
2
=25
Does not meet the circle x
2
+ y
2
= 25
Does not pass thro' the origin
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Question # 3
The axis of the parabola y
2
= 4ax is
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X = 0
Y = 0
X = y
X = -y
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Question # 4
The line Ax + By + C = 0 will touch the circle x
2
+ y
2
=
λ when
Choose an answer
C
2
=
λ
(A
2
+ B
2
)
A
2
=
λ
(A
2
+ C
2
)
B
2
=
λ
(A
2
+ C
2
)
None of these
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Question # 5
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Question # 6
Intersection of two parabolas
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parabola
Two points
Four points
Hyperobla
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Question # 7
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Question # 8
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 # 9
Two tangents drawn from (2,3) to the circle x2+y2 =9 are
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Real and distinct
Imaginary
Real and coincident
None of these
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Question # 10
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:
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y
2
= -4 ax
x
2
= 4ay
x
2
= -4ay
y
2
= 4ax
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Question # 11
The equation x2+ y2- 8x+ 6y+ 25= 0 represents
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A circle
A pair of straight lines
A point
None of these
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Question # 12
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 # 13
The locus of the centre of a circle which touches two given circles externally is:
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a hyperbola
an ellipse
a circle
a parabola
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Question # 14
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 # 15
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c = 0
c = -1
c = -2
c = 1
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Question # 16
If a > 0 they parabola y2 =-4ax lies in
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I and iv quadrant
I quadrant
II and III quadrant
All are incorrect
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Question # 17
The point where the axis meets the parabola is called
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Directrix
Foucu
Chord
Vertix
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Question # 18
The straight line passing through the focus and perpendicular to the directrix of the conic is known as its
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Tangent
axis
Focal chord
major or manor axis
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Question # 19
If the line 2x -y +k =0 is a diameter of the circle x2 +y2 +6x -6y +5 =0 then k is equal to
Choose an answer
12
9
6
3
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Question # 20
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 # 21
The line through the centre and perpendicular to the transverse axis is called the
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Major axis
Minor axis
Focal axis
Conjugate axis
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Question # 22
For the parabola the line through focus and perpendicular to the directrix is called
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Tangent
Vertex
Axis
None
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Question # 23
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Question # 24
The line joining the center of a circle to the midpoint of the chord is
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Perpendicular to the tnagent
Perpendicular to the normal
Perpendicular to the chord
Perpendicular to the chord
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Question # 25
The equation of the circle with centre origin and radius r is
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x
2
+ y
2
= 1
x
2
+ y
2
= r
2
x
2
+ y
2
= 0
x
2
- y
2
= r
2
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Question # 26
The length of the tangent from (2, 1) to the circle x
2
+ y
2
+ 4y + 3 = 0 is
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Question # 27
The parabola y2 + 2y + x = 0 lie in _____ quadrant.
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First
Second
Third
Fourth
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Question # 28
The vertex of the parabola (xsin a -ycos a)2 =4a(xcos a +ysin a) lies at
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(acos a,asin a)
(a,0)
(cos a,sin a)
(0,0)
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Question # 29
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A parabola
An ellipse
A hyperbola
A circle
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Question # 30
If a plane passes through the vertex of a cone then the intersection is
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an ellipse
a hyperbola
a point circle
a parabola
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Question # 31
Choose an answer
2 b
2 a
2 ab
a + b
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