JEE Questions for Maths Conic Section Quiz 4 - MCQExams.com


Maths-Conic Section-17196.png
  • √2/2
  • √3/2
  • 1/2
  • 3/4
Let S be the focus of the parabola y2 = 8x and PQ be the common chord of the circle x2 + y2 - 2x - 4y = 0 and the given parabola. The area of ∆OPS is
  • 6 sq units
  • 16 sq units
  • 4 sq units
  • 64 sq units
An ellipse is drawn by taking a diameter of the circle (x - 1)2 + y2 = 1 as its semi-minor axis and a diameter of the circle x2 + (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
  • 4x2 + y2 = 4
  • x2 + 4y2 = 8
  • 4x2 + y2 = 8
  • x2 + 4y2 = 16

Maths-Conic Section-17197.png
  • 1/4
  • 1/3
  • 1/2

  • Maths-Conic Section-17198.png
The line x = 2y intersects the ellipse x2/4 + y2 = 1 at the points P and Q. The equation of the circle with PQ as diameter is
  • x2 + y2 = 1/2
  • x2 + y2 = 1
  • x2 + y2 = 2
  • x2 + y2 = 5/2
Let P and Q are the points on the parabola y2 = 4x, 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
  • 1
  • 2
  • 4
  • 6
If the eccentricity of the hyperbola x2/a2 - y2/b2 = 1 is reciprocal to that of the ellipse x2 + 4y2 = 4. If the hyperbola passes through the focus of the ellipse, then
  • the equation of the hyperbola is x2 /3 - y2/2 = 1
  • a focus of the hyperbola is (2,
  • the eccentricity of the hyperbola is √(5/3)
  • 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
  • 5x2 + 3y2 - 48 = 0
  • 3x2 + 5y2 - 15 = 0
  • 5x2 + 3y2 - 32 = 0
  • 3x2 + 5y2 - 32 = 0
The circle x2 + y2 - 8x = 0 and hyperbola x2 /9 - y2/4 = 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
  • 2x - √5y - 20 = 0
  • 2x - √5y + 4 = 0
  • 3x - 4y + 8 = 0
  • 4x - 3y + 4 = 0
The circle x2 + y2 - 8x = 0 and hyperbola x2/9 - y2/4 = 1 intersect at the points A and B.
Equation of the circle with AB as its diameter is
  • x2 + y2 - 12x + 24 = 0
  • x2 + y2 + 12x + 24 = 0
  • x2 + y2 - 24x - 12 = 0
  • x2 + y2 - 24x - 12 = 0
The ellipse x2 + 4y2 = 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
  • x2 + 12y2 = 16
  • 4x2 + 48y2 = 48
  • 4x2 + 64y2 = 48
  • x2 + 16y2 = 16
Focus of hyperbola is (±3,and equation of tangent is 2x + y - 4 = 0, find the equation of hyperbola is
  • 4x2 - 5y2 = 20
  • 5x2 - 4y2 = 20
  • 4x2 - 5y2 = 1
  • 5x2 - 4y2 = 1
The circle x2 + y2 = a2 intersects the hyperbola xy = c2 in four points (xi, yi), for i = 1, 2, 3 and 4, then y1 + y2 + y3 + y4 equals
  • 0
  • c
  • a
  • c4
Consider the two curves C1 : y2 - 4x and C 2 : x2 + y2 - 6x + 1 = 0, then
  • C1 and C2 touch each other at only one point
  • C1 and C2 touch each other at exactly two points
  • C1 and C2 intersect (but do not touch ) at exactly two points
  • 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 y2 - 12x - 4y + 4 = 0. The equation of the parabola is
  • y2 - 8x - 6y + 25 = 0
  • y2 - 6x + 8y - 25 = 0
  • x2 - 6x - 8y + 25 = 0
  • x2 + 6x - 8y - 25 = 0

Maths-Conic Section-17200.png

  • Maths-Conic Section-17201.png
  • 2)
    Maths-Conic Section-17202.png

  • Maths-Conic Section-17203.png
  • None of these
x = 4 (1 + cos θ) and y = 3(1 + sinθ) are the parametric equations of

  • Maths-Conic Section-17204.png
  • 2)
    Maths-Conic Section-17205.png

  • Maths-Conic Section-17206.png

  • Maths-Conic Section-17207.png
The equation of the parabola whose focus i (3, -and directrix 6x - 7y + 5 = 0, is
  • (7x + 6y)2 - 570x + 750y + 2100 = 0
  • (7x + 6y)2 + 570x - 750y + 2100 = 0
  • (7x - 6y)2 - 570x + 750y + 2100 = 0
  • (7x - 6y)2 + 570x - 750y + 2100 = 0

Maths-Conic Section-17208.png
  • λ > 5
  • λ < 2
  • 2 < λ < 5
  • 2 > λ > 5
The locus of the mid - point of the line joining focus and any point on the parabola y2 = 4ax is a parabola with the equation of directrix as
  • x + a = 0
  • 2x + a = 0
  • x = 0
  • x = a/2
The two parabolas x2 = 4y and y2 = 4x meet in two distinct points. One of these is the origin and the other is
  • (2, 2)
  • (4, -4)
  • (4, 4)
  • (-2, 2)
The equation of the ellipse having vertices at (± 5,and foci (± 4,is

  • Maths-Conic Section-17210.png
  • 9x2 + 25y2 = 225

  • Maths-Conic Section-17211.png
  • 4x2 + 5y2 = 20
If r is a parameter then x = a(t + 1/t) and y = b(t - 1/t) represents
  • an ellipse
  • a circle
  • a pair of straight lines
  • hyperbola
The locus of the equation x2 - y2 = 0, is
  • a circle
  • a hyperbola
  • a pair of lines
  • a pair of lines at right angles
Length of the straight line x - 3y = 1 intercepted by the hyperbola x2 + 4y2 = 1 is
  • (3/√10
  • (6/√10
  • (5/√10
  • (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
  • 3x2 + 4y2 = 1
  • 3x2 + 4y2 = 12
  • 4x2 + 3y2 = 1
  • 4x2 + 3y2 = 12
If O is the origin and A is a point on the curve y2 = 4x. Then, the locus of the mid - point of OA, is
  • x2 = 4y
  • x2 = 2y
  • x2 = 16y
  • y2 = 2x
A hyperbola, having the transverse axis of length 2 sin 0, is confocal with the ellipse 3x2 + y2 = 12 then, its equation is
  • x2 cosec2 θ - y2 sec2 θ = 1
  • x2 sec2 θ - y2 cossec2 θ = 1
  • x2 sin2 θ - y2 cos2 θ = 1
  • x2 cos2 θ - y2 sin2 θ = 1
Equation of the parabola with its vertex at (1,and focus (3,is
  • (x -1)2 = 8 (y - 1)
  • (y -1)2 = 8 (x - 3)
  • (y -1)2 = 8 (x - 1)
  • (x -3)2 =8 (y - 1)
The curve described para metrically by x = t2 + 2t - 1, y = 3t + 5 represents
  • an ellipse
  • a hyperbola
  • a parabola
  • a circle
The equation of an ellipse whose eccentricity is 1/ 2 and the vertices are (4,and (10, 0), is
  • 3x2 + 4y2 - 42x + 120 = 0
  • 3x2 + 4y2 + 42x + 120 = 0
  • 3x2 + 4y2 + 42x - 120 = 0
  • 3x2 + 4y2 - 42x - 120 = 0

Maths-Conic Section-17213.png
  • (-3.lies on the hyperbola
  • (3,lies on the hyperbola
  • (10,lies on the hyperbola
  • (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
  • (1 + 3 cos θ, √3 sin θ)
  • (1 + 3 cos θ, 5 sin θ)
  • (1 + 3 cos θ, 1+ √5 sin θ)
  • (1 + 3 cos θ, 1 + 5 sin θ)
  • (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
  • an ellipse
  • a parabola
  • a hyperbola
  • a circle

Maths-Conic Section-17214.png
  • |t|< 2
  • |t| ≤ 1
  • |t|> 1
  • None of these
If P be the point (1,and Q a point on the locus of y2 = 8x. The locus of mid - point of PQ is
  • x2 - 4y + 2 = 0
  • x2 + 4y + 2 = 0
  • y2 + 4x + 2 = 0
  • y2 + 4x - 2 = 0

Maths-Conic Section-17215.png

  • Maths-Conic Section-17216.png
  • 2)
    Maths-Conic Section-17217.png

  • Maths-Conic Section-17218.png
  • 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
  • (x - y)2 = 8(x + y - 2)
  • (x + y)2 = 2(x + y - 2)
  • (x - y)2 = 4(x + y - 2)
  • (x + y)2 = 2(x - y + 2)

Maths-Conic Section-17219.png
  • xy = 3/4
  • xy = 35/16
  • xy = 64/105
  • 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

  • Maths-Conic Section-17220.png
  • 2)
    Maths-Conic Section-17221.png

  • Maths-Conic Section-17222.png

  • Maths-Conic Section-17223.png
The equation of the parabola with vertex at (0,and focus (2, 1), is
  • x2 - 2y - 12x - 11 = 0
  • x2 + 2y - 12x - 13 = 0
  • y2 - 2y + 12x +11 = 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

  • Maths-Conic Section-17224.png
  • 2)
    Maths-Conic Section-17225.png

  • Maths-Conic Section-17226.png

  • Maths-Conic Section-17227.png
Equation of the ellipse whose focii are (2,and (4,and the length of major axis is

  • Maths-Conic Section-17228.png
  • 2)
    Maths-Conic Section-17229.png

  • Maths-Conic Section-17230.png

  • Maths-Conic Section-17231.png
The equation of parabola with focus (0,and x + y = 4 is
  • x2 + y2 - 2xy + 8x + 8y - 16 = 0
  • x2 + y2 - 2xy + 8x + 8y= 0
  • x2 + y2 + 8x + 8y - 16 = 0
  • x2 + y2 + 8x + 8y + 16 = 0
The equation of the ellipse whose focii are (2,and eccentricity (1,is

  • Maths-Conic Section-17232.png
  • 2)
    Maths-Conic Section-17233.png

  • Maths-Conic Section-17234.png
  • None of these
If (0,and (0,are respectively the vertex and focus of a parabola, then its equation is
  • x2 + 12y = 72
  • x2 - 12y = 72
  • y2 - 12x = 72
  • y2 + 12x = 72
The curve with parametric x = et + e-t and y = et - e-t is
  • a circle
  • an ellipse
  • a hyperbola
  • a parabola
The equation of a parabola which passes through the intersection of a straight line x + y = 0 and the circle x2 + y2 + 4y = 0, is
  • y2 = 4x
  • y2 = x
  • y2 = 2x
  • None of these
The point (4, -with respect to the ellipse 4x2 + 5y2 = 1
  • a lies on the curve
  • is inside the curve
  • is outside of the curve
  • 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
  • 5x2 + 9y2 = 4
  • 2x2 - 6y2 = 28
  • 6x2 + 3y2 = 45
  • 9x2 + 5y2 = 180
0:0:1


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