Analytical Geometry Important Questions

11th Standard

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Answer all the questions

Time : 02:00:00 Hrs
Total Marks : 50
    10 x 1 = 10
  1. The angle between the pair of straight lines x2 - 7xy + 4y2 = 0

    (a)

    \(tan^{-1}\left(1\over 3\right)\)

    (b)

    \(tan^{-1}\left(1\over 2\right)\)

    (c)

    \(tan^{-1}\left(\sqrt{33}\over 5\right)\)

    (d)

    \(tan^{-1}\left(5\over\sqrt{33}\right)\)

  2. The slope of the line 7x + 5y - 8 = 0 is

    (a)

    7/5

    (b)

    -7/5

    (c)

    5/7

    (d)

    -9/7

  3. If kx2 + 3xy - 2y2 = 0 represent a pair of lines which are perpendicular then k is equal to

    (a)

    1/2

    (b)

    -1/2

    (c)

    2

    (d)

    -2

  4. The length of the tangent from (4,5) to the  circle x2 +y2 = 16 is

    (a)

    4

    (b)

    5

    (c)

    16

    (d)

    25

  5. The focus of the parabola x2 = 16y is

    (a)

    (4,0)

    (b)

    (-4,0)

    (c)

    (0,4)

    (d)

    (0,-4)

  6. Combined equation of co-ordinate axes is

    (a)

    x2-y2=0

    (b)

    x2+y2=0

    (c)

    xy=c

    (d)

    xy=0

  7. In the equation of the circle x2 +y2 = 16 then y-intercept is (are)

    (a)

    4

    (b)

    16

    (c)

    ±4

    (d)

    ±16

  8. The equation of the circle with centre (3,-4) and touches the x - axis

    (a)

    (x - 3)2 +(y - 4)2 = 4

    (b)

    (x - 3)2 +(y + 4)2 =16

    (c)

    (x-3)2+(y- 4)2=16

    (d)

    x2+y2=16

  9. The eccentricity of the parabola is

    (a)

    3

    (b)

    2

    (c)

    0

    (d)

    1

  10. The distance between directrix and focus of a parabola y2 = 4ax is

    (a)

    a

    (b)

    2a

    (c)

    4a

    (d)

    3a

  11. 5 x 2 = 10
  12. Find the equation of the circle whose centre is (-3, -2) and having circumferences 16\(\pi\)

  13. Find the acute angle between the lines 2x - y + 3 = 0 and x + y + 2 = 0.

  14. Find the angle between the pair of lines represented by the equation 3x2+10xy+8y2+14x+22y+15=0.

  15. For what value of k does 2x2+5xy+2y2+15x+18y+k=0 represent a pair of straight lines.

  16. Find the parametric equations of the circle x2+y2=25

  17. 5 x 3 = 15
  18. Find the angle between the lines whose slopes are \(\frac { 1 }{ 2 } \) and 3

  19. The parabola y2 = Kx passes through the point (4, -2) find its latus rectum and focus.

  20. Find the equation of the parabola whose focus is (-3, 2) and the directrix is x+y=4.

  21. Find the equation of the tangent lines to the circle x2+y2=9 which are parallel to 2x+y-3=0

  22. If the equation of a circle x2+y2+ax + by = 0 passing through the points (1, 2) and (1, 1), find the values of a and b

  23. 3 x 5 = 15
  24. Find the value of p for which the straight lines 8px+(2-3p)y+1 = 0 and px +py -7 =0 are perpendicular to each other.

  25. Find the equation of the parabola whose vertex is (0, 0) passing through the point (2, 3) and axis is along X-axis.

  26. Find the equation of the parabola whose focus is (1,3) and whose directrix is x-y+2=0.

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