Analytical Geometry - Important Question Paper

11th Standard

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Business Maths

Time : 01:00:00 Hrs
Total Marks : 50

    Part A

    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. If the lines 2x - 3y - 5 = 0 and 3x - 4y - 7 = 0 are the diameters of a circle, then its centre is

    (a)

    (-1, 1)

    (b)

    (1,1)

    (c)

    (1, -1 )

    (d)

    (-1, -1)

  3. The x - intercept of the straight line 3x + 2y - 1 = 0 is

    (a)

    3

    (b)

    2

    (c)

    1/3

    (d)

    1/2

  4. If the centre of the circle is (-a, -b) and radius \(\sqrt{a^2-b^2}\)then the equation of circle is

    (a)

    x2+y2+2ax+2by+2b2=0

    (b)

    x2+y2+2ax +2by-2b2=0

    (c)

    x2 +y2 - 2ax - 2by - 2b2 = 0

    (d)

    x2 + y - 2ax - 2by + 2b2 = 0

  5. Combined equation of co-ordinate axes is

    (a)

    x2-y2=0

    (b)

    x2+y2=0

    (c)

    xy=c

    (d)

    xy=0

  6. If the perimeter of the circle is 8π units and centre is (2,2) then the equation of the circle is

    (a)

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

    (b)

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

    (c)

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

    (d)

    x2 + y2 =4

  7. 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

  8. If the circle touches x axis, y axis and the line x = 6 then the length of the diameter of the circle is

    (a)

    6

    (b)

    3

    (c)

    12

    (d)

    4

  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. Part B

    6 x 2 = 12
  12. If A (-1,1) and B (2,3) are two fixed points, then find the locus of a point P So that the are of triangle APB = 8 Sq.units

  13. Find the equation of the following circles having the center (3,5) and radius 5 units

  14. Find the equation of the following circles having the center ( 0,0) and radius 2 units

  15. Find the center and radius of the circle  x2 + y2 - 22x - 4y + 25 = 0

  16. Find the center and radius of the circle 5x2 + 5y2 +4x - 8y - 16 = 0

  17. Find the focus, equation of the directrix, vertrix and length of latus sections of the parabola x2=6y.

  18. Part C

    6 x 3 = 18
  19. Find the equation of the parabola whose focus is (-3, 2) and the directrix is x+y=4.

  20. A point moves such that its distance from the point (4, 0) is half that of its distance from the line x = 16, find its locus.

  21. Prove that the lines (b - c) x + (c - a) y + (a - b) = 0, (c - a) x + (a - b) y + (b - c) = 0, and (a - b) x + (b - c) y+c-a=0 are concurrent.

  22. Find the slope of the lines which make an angle of 45° with the line 3x - y + 5 = 0.

  23. Find the combined equation of the straight line through the origin, one of which is parallel to and the other is perpendicular to the straight line 2x+y+1=0

  24. Find the equation of the circle having centre at (3, -4) and touching the line 5x +12y-12=0

  25. Part D

    2 x 5 = 10
  26. Show that the pair of straight lines 4x2 +12xy +9y2 -6x -9y +2 = 0 represents two parallel straight lines and also find the separate equations of the straight lines..

  27. Find the angle between the pair of straight lines 3x2 -5xy -2y2 +17x + y + 10 = 0

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