Analytical Geometry Model Question Paper

11th Standard

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Business Maths

Time : 01:00:00 Hrs
Total Marks : 50
    5 x 1 = 5
  1. If m1 and m2 are the slopes of the pair of lines given by ax2+ 2hxy + by2 = 0, then the value of m1 + m2 is

    (a)

    2h/b

    (b)

    -2h/b

    (c)

    2h/a

    (d)

    -2h/a

  2. 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

  3. Length of the latus rectum of the parabola y2 = - 25x is

    (a)

    25

    (b)

    -5

    (c)

    5

    (d)

    -25

  4. ax2 + 4xy + 2y2 = 0 represents a pair of parallel lines then 'a' is

    (a)

    2

    (b)

    -2

    (c)

    4

    (d)

    -4

  5. 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

  6. 5 x 2 = 10
  7. Find the equation of the circle whose centre is (2,3) and which passes through (1 , 4)

  8. Find the equation of the circle passing through the points (0, 1) , (4 ,3) and (1, -1)

  9. Find the combined equation of the given straight lines whose separate equations are 2x+y-1= 0 and x+2y-5= 0.

  10. Find the angle between the straight lines x2+4xy+y2=0

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

  12. 5 x 3 = 15
  13. Show that the straight lines x + y -4 = 0, 3x + 2 = 0 and 3x -3y + 16 = 0 are concurrent

  14. Find the value of 'a' for which the straight lines 3x +4y = 13; 2x -7y = -1  and ax - y -14 = 0 are concurrent

  15. Find the equation of the circle passing through the points (2, 3) and (-1, 1) and whose centre is on the line x-3y-11 = 0.

  16. Show that the pair of straight lines 4x2-12xy+9y2+18x-27y+8=0 represents a pair of parallel straight lines and find their separate equations.

  17. For what values of a and b does the equation (a-2)x2+by2+(b-2)xy+4x+4y-1=0 represents a circle? Write down the resulting equation of the circle.

  18. 4 x 5 = 20
  19. Find whether the points (-1,-2), (1,0) and (-3, -4) lie above, below or on the line 3x+2y+7 =0.

  20. If (4,1) is one extremity of a diameter of the circle x2 +y2 - 2x + 6y -15 = 0, find the other extremity

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

  22. If a parabolic reflector is 20 cm in diameter and 5 cm deep, find the focus.

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