Two Dimensional Analytical Geometry-II Book Back Questions

12th Standard EM

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Maths

Time : 00:45:00 Hrs
Total Marks : 30
    5 x 1 = 5
  1. The equation of the circle passing through(1,5) and (4,1) and touching y -axis is x2+y2−5x−6y+9+(4x+3y−19)=0 whereλ is equal to

    (a)

    \(0,-\frac { 40 }{ 9 } \)

    (b)

    0

    (c)

    \(\frac { 40 }{ 9 } \)

    (d)

    \(\frac { -40 }{ 9 } \)

  2. The radius of the circle3x2+by2+4bx−6by+b2 =0 is

    (a)

    1

    (b)

    3

    (c)

    \( \sqrt {10}\)

    (d)

    \( \sqrt {11}\)

  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. The ellipse E1\(\frac { { x }^{ 2 } }{ 9 } +\frac { { y }^{ 2 } }{ 4 } =1\) is inscribed in a rectangle R whose sides are parallel to the coordinate axes. Another ellipse E2 passing through the point(0,4) circumscribes the rectangle R . The eccentricity of the ellipse is

    (a)

    \(\frac { \sqrt { 2 } }{ 2 } \)

    (b)

    \(\frac { \sqrt { 3 } }{ 2 } \)

    (c)

    \(\frac { 1 }{ 2 } \)

    (d)

    \(\frac { 3 }{ 4 } \)

  5. Tangents are drawn to the hyperbola  \(\frac { { x }^{ 2 } }{ 9 } +\frac { { y }^{ 2 } }{ 4 } =1\) 1parallel to the straight line2x−y=1. One of the points of contact of tangents on the hyperbola is

    (a)

    \(\frac { 9 }{ 2\sqrt { 2 } } ,\frac { -1 }{ \sqrt { 2 } } \)

    (b)

    \(\frac { -9 }{ 2\sqrt { 2 } } ,\frac { 1 }{ \sqrt { 2 } } \)

    (c)

    \(\frac { 9 }{ 2\sqrt { 2 } } ,\frac { 1 }{ \sqrt { 2 } } \)

    (d)

    \(\left( 3\sqrt { 3 } ,-2\sqrt { 2 } \right) \)

  6. 3 x 2 = 6
  7. Obtain the equation of the circle for which (3,4) and (2,-7) are the ends of a diameter.

  8. 11x2−25y2−44x+50y−256 = 0

  9. Find centre and radius of the following circles.
    2x2+2y2−6x+4y+2=0

  10. 3 x 3 = 9
  11. Find the equation of the circle with centre (2,3) and passing through the intersection of the lines 3x−2y−1=0and 4x+y−27=0.

  12. Identify the type of the conic for the following equations:
    (1) 16y2=−4x2+64
    (2) x2+y2=−4x−y+4
    (3) x2−2y=x+3
    (4) 4x2−9y2−16x+18y−29 = 0

  13. The parabolic communication antenna has a focus at 2m distance from the vertex of the antenna. Find the width of the antenna 3m from the vertex.

  14. 2 x 5 = 10
  15. 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.

  16. Identify the type of conic and find centre, foci, vertices, and directrices of each of the following :
    18x2+12y2−144x+48y+120 = 0

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