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Two Dimensional Analytical Geometry II Model Question Paper

12th Standard EM

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Maths

Time : 01:00:00 Hrs
Total Marks : 50
    5 x 1 = 5
  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 centre of the circle inscribed in a square formed by the lines x2−8x−12=0 and y2−14y+45 = 0 is

    (a)

    (4,7)

    (b)

    (7,4)

    (c)

    (9,4)

    (d)

    (4,9)

  3. If P(x, y) be any point on 16x2+25y2=400 with foci F1 (3,0) and F2 (-3,0) then PF1 PF2 +
    is

    (a)

    8

    (b)

    6

    (c)

    10

    (d)

    12

  4. If the normals of the parabola y2 = 4x drawn at the end points of its latus rectum are tangents to the circle (x−3)2+(y+2)2=r2 , then the value of r2 is

    (a)

    2

    (b)

    3

    (c)

    1

    (d)

    4

  5. 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)

  6. 5 x 2 = 10
  7. If y=4x+c is a tangent to the circle x2+y2=9 , find c .

  8. Obtain the equation of the circles with radius 5 cm and touching x-axis at the origin in general form.

  9. Obtain the equation of the circle for which (3,4) and (2,-7) are the ends of a diameter.

  10. Find the locus of a point which divides so that the sum of its.distances from (-4, 0) and (4, 0) is 10 units.

  11. Find the equation of the hyperbola whose vertices are (0, ±7) and e = \(\frac { 4 }{ 3 } \)

  12. 5 x 3 = 15
  13. Find the equations of the tangent and normal to the circle x2+y2=25 at P(-3,4).

  14. Find the equation of circles that touch both the axes and pass through (-4,-2) in general form.

  15. Find the equation of the hyperbola with vertices (0,±4) and foci(0,±6).

  16. Find the equations of tangent and normal to the ellipse x2+4y2=32 when \(\theta =\frac { \pi }{ 4 } \)

  17. For the hyperbola 3x2 - 6y2 = -18, find the length of transverse and conjugate axes and eccentricity.

  18. 4 x 5 = 20
  19. Find the equation of the ellipse whose eccentricity is \(\frac { 1 }{ 2 } \), one of the foci is(2,3) and a directrix is x = 7 . Also find the length of the major and minor axes of the ellipse.

  20. Find the centre, foci, and eccentricity of the hyperbola 11x2−25y2−44x+50y−256 = 0

  21. An equilateral triangle is inscribed in the parabola y2 = 4ax whose vertex is at the vertex of the parabola. Find the length of its side.

  22. The foci of a hyperbola coincides with the foci of the ellipse \(\frac { { x }^{ 2 } }{ 25 } +\frac { y^{ 2 } }{ 9 } =1\). Find the equation of the hyperbola if its eccentricity is 2.

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