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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 conic is a parabola if
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e < 1
e > 1
e = 1
None of these
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Question # 3
The equation of vertical asymptotes of y = cos ecx is
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x = 0
y = 0
x =∞
y =∞
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Question # 4
The second degree equation 2x2 -xy+ 5x -2y +2 =0 represents
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Circle
Hyperbola
Ellipse
Pair of straight lines
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Question # 5
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 # 6
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Question # 7
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Question # 8
y=-a is the equation of the directrix of
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y2 =4ax
x2=-4ay
x2=4ay
y2=-4ax
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Question # 9
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Question # 10
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 # 11
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 # 12
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Question # 13
The span of a standard parabola depends upon
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x
a
y
y2
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Question # 14
I f the focus is F ( 0,-a) and directrix is the line v=a, then equation of the parabola is:
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x
2
= 4ay
y
2
= 4ax
y
2
= -4ax
x
2
= 4ax
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Question # 15
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none of these
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Question # 16
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 # 17
Ifᵨ> 1 , then the conic, is:
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Ellipse
Parabola
Hyperbola
None of these
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Question # 18
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 # 19
The line Ax + By + C = 0 will touch the circle x
2
+ y
2
=
λ when
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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 # 20
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 # 21
The area of the circle centred at (1,2) and passing through (4,6) is
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30 πsq.units
5π sq.units
15π sq.units
25π sq.units
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Question # 22
If (2,0) is the vertex and y-axis is directrix of parabola then focus is
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(2,0)
(-2,0)
(4,0)
(-4,0)
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Question # 23
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 # 24
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Question # 25
The tangents drawn from the point P to a circle are real and distinct if
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P is on the circle
P is inside the circle
P is outside the circle
none of these
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Question # 26
Equation of the chord of contact to the tangents drawn from (-3,4) to the circle x2 + y2 = 21
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-3x + 4y =21
4x - 3x = 0
-3x + 4y = 25
None of these
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Question # 27
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 # 28
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 # 29
The parametric equations of a circle are
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Question # 30
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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