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JEE Questions for Maths Conic Section Quiz 4 - MCQExams.com
JEE
Maths
Conic Section
Quiz 4
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0%
√2/2
0%
√3/2
0%
1/2
0%
3/4
Let S be the focus of the parabola y
2
= 8
x
and PQ be the common chord of the circle
x
2
+ y
2
- 2
x
- 4y = 0 and the given parabola. The area of ∆OPS is
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0%
6 sq units
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16 sq units
0%
4 sq units
0%
64 sq units
An ellipse is drawn by taking a diameter of the circle (
x
- 1)
2
+ y
2
= 1 as its semi-minor axis and a diameter of the circle
x
2
+ (y - 2)
2
= 4 is semi - major axis, if the centre of the ellipse at the origin and its axis are the coordinates axes, then the equation of the ellipse is
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0%
4x2 + y2 = 4
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x2 + 4y2 = 8
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4x2 + y2 = 8
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x2 + 4y2 = 16
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1/4
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1/3
0%
1/2
0%
The line
x
= 2y intersects the ellipse
x
2
/4 + y
2
= 1 at the points P and Q. The equation of the circle with PQ as diameter is
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x2 + y2 = 1/2
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x2 + y2 = 1
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x2 + y2 = 2
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x2 + y2 = 5/2
Let P and Q are the points on the parabola y
2
= 4
x
, if so that the line segment PQ subtends right angle at the vertex. If PQ intersects the axis of the parabola at R, then the distance of the vertex from R is
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0%
1
0%
2
0%
4
0%
6
If the eccentricity of the hyperbola
x
2
/a
2
- y
2
/b
2
= 1 is reciprocal to that of the ellipse
x
2
+ 4y
2
= 4. If the hyperbola passes through the focus of the ellipse, then
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0%
the equation of the hyperbola is x2 /3 - y2/2 = 1
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a focus of the hyperbola is (2,
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the eccentricity of the hyperbola is √(5/3)
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the equation of the hyperbola is x2 - 3y2 = 3
Equation of the ellipse whose axes are the axes of coordinates and which passes through the point (-3,and has eccentricity √(2/is
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5x2 + 3y2 - 48 = 0
0%
3x2 + 5y2 - 15 = 0
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5x2 + 3y2 - 32 = 0
0%
3x2 + 5y2 - 32 = 0
The circle
x
2
+ y
2
- 8
x
= 0 and hyperbola
x
2
/9 - y
2
/4 = 1 intersect at the points A and B. Equation of a common tangent with positive slope to the circle as well as to the hyperbola is
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0%
2x - √5y - 20 = 0
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2x - √5y + 4 = 0
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3x - 4y + 8 = 0
0%
4x - 3y + 4 = 0
The circle
x
2
+ y
2
- 8
x
= 0 and hyperbola
x
2
/9 - y
2
/4 = 1 intersect at the points A and B. Equation of the circle with AB as its diameter is
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0%
x2 + y2 - 12x + 24 = 0
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x2 + y2 + 12x + 24 = 0
0%
x2 + y2 - 24x - 12 = 0
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x2 + y2 - 24x - 12 = 0
The ellipse
x
2
+ 4y
2
= 4 is inscribed in a rectangle aligned with the coordinate axes, which is turn in inscribed in another ellipse that passes through the point (4, 0). Then, the equation of the ellipse is
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0%
x2 + 12y2 = 16
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4x2 + 48y2 = 48
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4x2 + 64y2 = 48
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x2 + 16y2 = 16
Focus of hyperbola is (±3,and equation of tangent is 2
x
+ y - 4 = 0, find the equation of hyperbola is
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0%
4x2 - 5y2 = 20
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5x2 - 4y2 = 20
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4x2 - 5y2 = 1
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5x2 - 4y2 = 1
The circle
x
2
+ y
2
= a
2
intersects the hyperbola
x
y = c
2
in four points (
x
i
, y
i
), for i = 1, 2, 3 and 4, then y
1
+ y
2
+ y
3
+ y
4
equals
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0%
0
0%
c
0%
a
0%
c4
Consider the two curves C
1
: y
2
- 4
x
and C
2
:
x
2
+ y
2
- 6
x
+ 1 = 0, then
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C1 and C2 touch each other at only one point
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C1 and C2 touch each other at exactly two points
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C1 and C2 intersect (but do not touch ) at exactly two points
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C1 and C2 neither intersect nor touch each other
A parabola is drawn with its focus at (3,and vertex at the focus of the parabola y
2
- 12
x
- 4y + 4 = 0. The equation of the parabola is
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0%
y2 - 8x - 6y + 25 = 0
0%
y2 - 6x + 8y - 25 = 0
0%
x2 - 6x - 8y + 25 = 0
0%
x2 + 6x - 8y - 25 = 0
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0%
0%
2)
0%
0%
None of these
x
= 4 (1 + cos θ) and y = 3(1 + sinθ) are the parametric equations of
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0%
0%
2)
0%
0%
The equation of the parabola whose focus i (3, -and directrix 6
x
- 7y + 5 = 0, is
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0%
(7x + 6y)2 - 570x + 750y + 2100 = 0
0%
(7x + 6y)2 + 570x - 750y + 2100 = 0
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(7x - 6y)2 - 570x + 750y + 2100 = 0
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(7x - 6y)2 + 570x - 750y + 2100 = 0
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λ > 5
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λ < 2
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2 < λ < 5
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2 > λ > 5
The locus of the mid - point of the line joining focus and any point on the parabola y
2
= 4a
x
is a parabola with the equation of directrix as
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x + a = 0
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2x + a = 0
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x = 0
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x = a/2
The two parabolas
x
2
= 4y and y
2
= 4
x
meet in two distinct points. One of these is the origin and the other is
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0%
(2, 2)
0%
(4, -4)
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(4, 4)
0%
(-2, 2)
The equation of the ellipse having vertices at (± 5,and foci (± 4,is
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0%
9x2 + 25y2 = 225
0%
0%
4x2 + 5y2 = 20
If r is a parameter then
x
= a(t + 1/t) and y = b(t - 1/t) represents
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an ellipse
0%
a circle
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a pair of straight lines
0%
hyperbola
The locus of the equation
x
2
- y
2
= 0, is
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0%
a circle
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a hyperbola
0%
a pair of lines
0%
a pair of lines at right angles
Length of the straight line
x
- 3y = 1 intercepted by the hyperbola
x
2
+ 4y
2
= 1 is
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0%
(3/√10
0%
(6/√10
0%
(5/√10
0%
(5/√10
For an ellipse with eccentricity 1/2 the centre is at the origin. If one directrix is
x
= 4, then the equation of the ellipse is
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0%
3x2 + 4y2 = 1
0%
3x2 + 4y2 = 12
0%
4x2 + 3y2 = 1
0%
4x2 + 3y2 = 12
If O is the origin and A is a point on the curve y
2
= 4
x
. Then, the locus of the mid - point of OA, is
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x2 = 4y
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x2 = 2y
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x2 = 16y
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y2 = 2x
A hyperbola, having the transverse axis of length 2 sin 0, is confocal with the ellipse 3
x
2
+ y
2
= 12 then, its equation is
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x2 cosec2 θ - y2 sec2 θ = 1
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x2 sec2 θ - y2 cossec2 θ = 1
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x2 sin2 θ - y2 cos2 θ = 1
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x2 cos2 θ - y2 sin2 θ = 1
Equation of the parabola with its vertex at (1,and focus (3,is
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(x -1)2 = 8 (y - 1)
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(y -1)2 = 8 (x - 3)
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(y -1)2 = 8 (x - 1)
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(x -3)2 =8 (y - 1)
The curve described para metrically by
x
= t
2
+ 2t - 1, y = 3t + 5 represents
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0%
an ellipse
0%
a hyperbola
0%
a parabola
0%
a circle
The equation of an ellipse whose eccentricity is 1/ 2 and the vertices are (4,and (10, 0), is
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0%
3x2 + 4y2 - 42x + 120 = 0
0%
3x2 + 4y2 + 42x + 120 = 0
0%
3x2 + 4y2 + 42x - 120 = 0
0%
3x2 + 4y2 - 42x - 120 = 0
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(-3.lies on the hyperbola
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(3,lies on the hyperbola
0%
(10,lies on the hyperbola
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(5,lies on the hyperbola
The parametric representation of a point of the ellipse whose foci are (3,and (-1,and eccentricity 2/3 is
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(1 + 3 cos θ, √3 sin θ)
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(1 + 3 cos θ, 5 sin θ)
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(1 + 3 cos θ, 1+ √5 sin θ)
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(1 + 3 cos θ, 1 + 5 sin θ)
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(1 + 3 cos θ, √5 sin θ)
The curve represented by
x
= 3 (cos t + sin t) and y = 4(cos t - sin t) is
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0%
an ellipse
0%
a parabola
0%
a hyperbola
0%
a circle
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0%
|t|< 2
0%
|t| ≤ 1
0%
|t|> 1
0%
None of these
If P be the point (1,and Q a point on the locus of y
2
= 8
x
. The locus of mid - point of PQ is
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x2 - 4y + 2 = 0
0%
x2 + 4y + 2 = 0
0%
y2 + 4x + 2 = 0
0%
y2 + 4x - 2 = 0
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0%
0%
2)
0%
0%
None of these
Axis of a parabola is y =
x
and vertex and focus are at a distance √2 and 2√2, respectively from the origin. Then, equation of the parabola is
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(x - y)2 = 8(x + y - 2)
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(x + y)2 = 2(x + y - 2)
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(x - y)2 = 4(x + y - 2)
0%
(x + y)2 = 2(x - y + 2)
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xy = 3/4
0%
xy = 35/16
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xy = 64/105
0%
xy = 105/64
The equation of the hyperbola in the standard form (with transverse axis along the x - axis) having the length of the latusrectum = 9 units and eccentricity = 5/4 is
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0%
0%
2)
0%
0%
The equation of the parabola with vertex at (0,and focus (2, 1), is
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x2 - 2y - 12x - 11 = 0
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x2 + 2y - 12x - 13 = 0
0%
y2 - 2y + 12x +11 = 0
0%
y2 - 2y - 12x + 13 = 0
The equation of the hyperbola whose vertices are (5,and (5,and one of the distance is
x
- 25/7 is
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0%
0%
2)
0%
0%
Equation of the ellipse whose focii are (2,and (4,and the length of major axis is
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0%
0%
2)
0%
0%
The equation of parabola with focus (0,and
x
+ y = 4 is
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0%
x2 + y2 - 2xy + 8x + 8y - 16 = 0
0%
x2 + y2 - 2xy + 8x + 8y= 0
0%
x2 + y2 + 8x + 8y - 16 = 0
0%
x2 + y2 + 8x + 8y + 16 = 0
The equation of the ellipse whose focii are (2,and eccentricity (1,is
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0%
0%
2)
0%
0%
None of these
If (0,and (0,are respectively the vertex and focus of a parabola, then its equation is
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x2 + 12y = 72
0%
x2 - 12y = 72
0%
y2 - 12x = 72
0%
y2 + 12x = 72
The curve with parametric
x
= e
t
+ e
-t
and y = e
t
- e
-t
is
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0%
a circle
0%
an ellipse
0%
a hyperbola
0%
a parabola
The equation of a parabola which passes through the intersection of a straight line
x
+ y = 0 and the circle
x
2
+ y
2
+ 4y = 0, is
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0%
y2 = 4x
0%
y2 = x
0%
y2 = 2x
0%
None of these
The point (4, -with respect to the ellipse 4
x
2
+ 5y
2
= 1
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0%
a lies on the curve
0%
is inside the curve
0%
is outside of the curve
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is focus of the curve
The foci of an ellipse are (0, ±and the equations for the directrices are y = ± 9. The equation for the ellipse is
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0%
5x2 + 9y2 = 4
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2x2 - 6y2 = 28
0%
6x2 + 3y2 = 45
0%
9x2 + 5y2 = 180
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