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Two Dimensional Analytical Geometry-II 5 Mark Creative Question Paper With Answer Key

12th Standard

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Maths

Time : 01:00:00 Hrs
Total Marks : 75

    5 Marks

    15 x 5 = 75
  1. Find the equation of the tangent at t = 1 to the parabola y2 = 12x

  2. Find the equations of the two tangents that can be drawn from the point (5, 2) to the ellipse 2x2 +7y2 = 14.

  3. Find the vertex, focus, directrix, axis and latus rectum of the parabola \(y^{2}-4 x-4 y=0\)

  4. Find the equation of the ellipse given that the centre is (4, -1), focus is (1, -1) and passing through (8, 0).

  5. Find the equation of a point which moves so that the sum of its distances ftom (- 4, 0) and (4, 0) is 10.

  6. Find the equations of axes and length of axes of the ellipse \(6 x^{2}+9 y^{2}+12 x-36 y-12=0\)

  7. Find the equations of directrices, latus rectum and length of latus rectums of the following ellipse \(4 x^{2}+3 y^{2}+8 x+12 y+4=0\)

  8. Find the centre, foci and eccentricity of the hyperbola \(12 x^{2}-4 y^{2}-24 x+32 y-124=0\)

  9. Find the equation of the ellipse whose eccentricity is \(\frac{4}{5}\) and axes are along the co-ordinate axes and with foci at \((0, \pm 4)\)

  10. Determine the equation of the ellipse whose directrices along y = \(\pm\)9 and foci at (0, \(\pm\)4). Also find the length of its latus rectum.

  11. The co-ordinates of the vertices of a hyperbola are (9, 2) and (1, 2) and the distance between its two foci is 10. Find its equation and also the length of its latus rectum.

  12. Find the equation of the hyperbola whose co- ordinates of the foci of a hyperbola are (±6, 0) and its latus rectum is of 10 units.

  13. The girder of a railway bridge is in the parabolic or with span 100 ft. and the highest point on the arch is 10 ft. above the bridge. Find the height of the bridge at 10 ft. to the left or right from the midpoint of the bridge.

  14. A reflecting telescope has a parabolic mirror for which the distance from the vertex to the focus in 9 mts. If the distance across (diameter) the top of the mirror is 160 cm, how deep is the mirror at the middle?

  15. A  comet is moving in a parabolic orbit around the sun which is at the focus of a parabola. When the comet is 80 million kms from the sun, the line segment from the sun to the comet makes an angle of \(\frac{\pi}{3}\) radians with the axis of the orbit. Find
    (i) the equation of the comet's orbit
    (ii) how close does the comet come nearer to sun? (Take the orbit as open rightward).

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