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12th Standard Maths Two Dimensional Analytical Geometry-II English Medium Free Online Test One Mark Questions with Answer Key 2020 - 2021

12th Standard

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Maths

Time : 00:10:00 Hrs
Total Marks : 10

    Answer all the questions

    10 x 1 = 10
  1. The eccentricity of the hyperbola whose latus rectum is 8 and conjugate axis is equal to half the distance between the foci is

    (a)

    \(\frac { 4 }{ 3 } \)

    (b)

    \(\frac { 4 }{ \sqrt { 3 } } \)

    (c)

    \(\frac { 2 }{ \sqrt { 3 } } \)

    (d)

    \(\frac { 3 }{ 2 } \)

  2. The area of quadrilateral formed with foci of the hyperbolas \(\frac { { x }^{ 2 } }{ { a }^{ 2 } } -\frac { { y }^{ 2 } }{ { b }^{ 2 } } =1\\ \) and \(\frac { { x }^{ 2 } }{ { a }^{ 2 } } -\frac { { y }^{ 2 } }{ { b }^{ 2 } } =-1\)

    (a)

    4(a2+b2)

    (b)

    2(a2+b2)

    (c)

    a2 +b2

    (d)

    \(\frac { 1 }{ 2 } \)(a2+b2)

  3. Tangents are drawn to the hyperbola  \(\frac { { x }^{ 2 } }{ 9 } +\frac { { y }^{ 2 } }{ 4 } =1\) 1parallel to the straight line2x−y=1. One of the points of contact of tangents on the hyperbola is

    (a)

    \(\frac { 9 }{ 2\sqrt { 2 } } ,\frac { -1 }{ \sqrt { 2 } } \)

    (b)

    \(\frac { -9 }{ 2\sqrt { 2 } } ,\frac { 1 }{ \sqrt { 2 } } \)

    (c)

    \(\frac { 9 }{ 2\sqrt { 2 } } ,\frac { 1 }{ \sqrt { 2 } } \)

    (d)

    \(\left( 3\sqrt { 3 } ,-2\sqrt { 2 } \right) \)

  4. Area of the greatest rectangle inscribed in the ellipse \(\frac { { x }^{ 2 } }{ { a }^{ 2 } } +\frac { { y }^{ 2 } }{ { b }^{ 2 } } =1.\) is

    (a)

    2ab

    (b)

    ab

    (c)

    \( \sqrt{ ab}\)

    (d)

    \(\frac { a }{ b } \)

  5. The values of m for which the line y=mx+ \(2\sqrt { 5 } \) touches the hyperbola 16x2−9y2=144 are the roots of x2−(a+b)x−4=0, then the value of (a+b) is

    (a)

    2

    (b)

    4

    (c)

    0

    (d)

    -2

  6. The equation of the directrix of the parabola y2+ 4y + 4x + 2 = 0 is

    (a)

    x = -1

    (b)

    x = 1

    (c)

    x = \(\frac{-3}{2}\)

    (d)

    x = \(\frac{3}{2}\)

  7. If the distance between the foci is 2 and the distance between the direction is 5, then the equation of the ellipse is

    (a)

    6x2 + 10y2 = 5

    (b)

    6x2 + 10y2 = 15

    (c)

    x2 + 3y2 = 10

    (d)

    none

  8. The length of major and minor axes of 4x2 + 3y2 = 12 are ____________

    (a)

    4, 2\(\sqrt3\)

    (b)

    2, \(\sqrt3\)

    (c)

    2\(\sqrt3\), 4

    (d)

    \(\sqrt3\), 2

  9. The locus of the foot of perpendicular from the focus on any tangent to y2 = 4ax is

    (a)

    x2 + y2 = a2 - b2

    (b)

    x2 + y2 = a2

    (c)

    x2 + y2 = a2 - b2

    (d)

    x = 0

  10. The locus of the point of intersection of perpendicular tangents of the parabola y2 = 4ax is

    (a)

    latus rectum

    (b)

    directrix

    (c)

    tangent at the vertex

    (d)

    axis of the parabola

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