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Two Dimensional Analytical Geometry II One Mark Questions with Answer

12th Standard EM

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Maths

Time : 00:45:00 Hrs
Total Marks : 25
    25 x 1 = 25
  1. 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 = \(\frac{3}{2}\)

  2. Equation of tangent at (-4, -4) on x2 = -4y is

    (a)

    2x - y + 4 = 0

    (b)

    2x + y - 4 = 0

    (c)

    2x - y - 12 = 0

    (d)

    2x + y + 4 = 0

  3. If a parabolic reflector is 20 em in diameter and 5 em deep, then its focus is

    (a)

    (0,5)

    (b)

    (5,0)

    (c)

    (10,0)

    (d)

    (0, 10)

  4. The eccentricity of the ellipse 9x2+ 5y2 - 30y= 0 is

    (a)

    \(\frac13\)

    (b)

    \(\frac23\)

    (c)

    \(\frac34\)

    (d)

    none of these

  5. The length of the latus rectum of the ellipse \(\frac { { x }^{ 2 } }{ 36 } +\frac { { y }^{ 2 } }{ 49 } \) = 1 is

    (a)

    \(\frac { 98 }{ 6 } \)

    (b)

    \(\frac { 72 }{ 7 } \)

    (c)

    \(\frac { 72 }{ 14 } \)

    (d)

    \(\frac { 98 }{ 12 } \)

  6. In an ellipse, the distance between its foci is 6 and its minor axis is 8, then e is

    (a)

    \(\frac { 4 }{ 5 } \)

    (b)

    \(\frac { 1 }{ \sqrt { 52 } } \)

    (c)

    \(\frac { 3 }{ 5 } \)

    (d)

    \(\frac { 1 }{ 2 } \)

  7. The equation 7x2- 6\(\sqrt { 3 } \) xy + 13y2 - 4\(\sqrt { 3 } \) x - 4y - 12 = 0 represents

    (a)

    parabola

    (b)

    ellipse

    (c)

    hyperbola

    (d)

    rectangular hyperbola

  8. The distance between the foci of a hyperbola is 16 and e = \(\sqrt { 2 } \) Its equation is

    (a)

    x2 - y2 = 32

    (b)

    y2 - x2 = 32

    (c)

    x2 - y2 = 16

    (d)

    y2 - x2 = 16

  9. When the eccentricity of a ellipse becomes zero, then it becomes a

    (a)

    straight line

    (b)

    circle

    (c)

    point

    (d)

    parabola

  10. The auxiliary circle of the ellipse \(\frac { { x }^{ 2 } }{ 25 } +\frac { { y }^{ 2 } }{ 16 } \) = 1 is

    (a)

    x2 + y2 = 25

    (b)

    x2 + y2 = 16

    (c)

    x2 + y2 = 41

    (d)

    x2 + y2 = 5

  11. The length of the diameter of a circle with centre (1, 2) and passing through (5, 5) is

    (a)

    5

    (b)

    \(\sqrt{45}\)

    (c)

    10

    (d)

    \(\sqrt{50}\)

  12. If (1, -3) is the centre of the circle x+ y+ ax + by + 9 = 0 its radius is

    (a)

    \(\sqrt{10}\)

    (b)

    1

    (c)

    5

    (d)

    \(\sqrt{19}\)

  13. The equation of tangent at (1, 2) to the circle x+ y2 = 5 is

    (a)

    x+y=3

    (b)

    x + 2y = 3

    (c)

    x- y= 5

    (d)

    x - 2y = 5

  14. If y = 2x + c is a tangent to the circle x2 + y2 = 5, then c is

    (a)

    土5

    (b)

    \(\sqrt5\)

    (c)

    土5\(\sqrt2\)

    (d)

    ±2\(\sqrt5\)

  15. The line y = mx +1 is a tangent to the parabola y2 = 4x if m = ______________

    (a)

    1

    (b)

    2

    (c)

    3

    (d)

    4

  16. The angle between the tangents drawn from (1, 4) to the parabola y2 = 4x is __________

    (a)

    \(\frac { \pi }{ 2 } \)

    (b)

    \(\frac { \pi }{ 3 } \)

    (c)

    \(\frac { \pi }{ 5 } \)

    (d)

    \(\frac { \pi }{ 5 } \)

  17. In an ellipse 5x2 + 7y2 = 11, the point (4, -3) lies _________ the ellipse

    (a)

    on

    (b)

    outside

    (c)

    inside

    (d)

    none

  18. The number of normals to the hyperbola \(\frac { { x }^{ 2 } }{ { a }^{ 2 } } +\frac { { y }^{ 2 } }{ { b }^{ 2 } } \) = 1 from an external point is

    (a)

    2

    (b)

    4

    (c)

    6

    (d)

    5

  19. The point of contact of y2 = 4ax and the tangent y = mx + c is

    (a)

    \(\left( \frac { 2a }{ { m }^{ 2 } } ,\frac { a }{ m } \right) \)

    (b)

    \(\left( \frac { a }{ { m }^{ 2 } } ,\frac { 2a }{ m } \right) \)

    (c)

    \(\left( \frac { a }{ m} ,\frac { 2a }{ { m }^{ 2 } } \right) \)

    (d)

    \(\left( \frac {-a }{ { m }^{ 2 }} ,\frac {- 2a }{ m } \right) \)

  20. If B, B1 are the ends of minor axis, F1 ,F2 are foci of the ellipse \(\frac { { x }^{ 2 } }{ 8 } +\frac { { y }^{ 2 } }{ 4 } \) = 1 then area of F1BF2B1 is

    (a)

    16

    (b)

    8

    (c)

    16\(\sqrt2\)

    (d)

    32\(\sqrt2\)

  21. 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

  22. The tangent at any point P on the ellipse \(\frac { { x }^{ 2 } }{ 6 } +\frac { { y }^{ 2 } }{ 3 } \) = 1 whose centre C meets the major axis at T and PN is the perpendicular to the major axis; The CN CT = ______________

    (a)

    \(\sqrt6\)

    (b)

    3

    (c)

    \(\sqrt3\)

    (d)

    6

  23. The locus of the point of Inter eetton of perpendicular tangents to the hyperbela \(\frac { { x }^{ 2 } }{ 16 } +\frac { { y }^{ 2 } }{ 9 } \) = 1 is __________

    (a)

    x2+y2= 25

    (b)

    x2 +y2 = 4.

    (c)

    x2 +y2 = 3

    (d)

    x2+y2=7

  24. Th point of curve y = 2x2 - 6x - 4 at which the targent is parallel to x - axis is

    (a)

    \(\left( \frac { 5 }{ 2 } ,\frac { -7 }{ 12 } \right) \)

    (b)

    \(\left( \frac { -5 }{ 2 } ,\frac { -7 }{ 2 } \right) \)

    (c)

    \(\left( \frac { -5 }{ 2 } ,\frac { 17 }{ 12 } \right) \)

    (d)

    \(\left( \frac { 3 }{ 2 } ,\frac { -7 }{ 2 } \right) \)

  25. 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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