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Conic Sections Test - 6

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Conic Sections Test - 6
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Weekly Quiz Competition
  • Question 1
    2 / -0.83

    The radius of the circle passing through the foci of the ellipse   and having its centre at (0, 3) is

    Solution

  • Question 2
    2 / -0.83

    The line y = c is a tangent to the parabola 7/2  if c is equal to

    Solution

    y = x is tangent to the parabola
    y=ax2 +c
    if a= then c=?
    y ′=2ax
    y ’= 2(7/2)x  =1
    x = 1/7
    1/7 = 2(1/7)2 + c
    c = 1/7 * 2/49
    c = 7/2

  • Question 3
    2 / -0.83

    The equation  2x2 +3y2 −8x −18y+35 = λRepresents

    Solution

    Given the equation is,
    2x2 +3y2 −8x −18y+35=K
    Or, 2{x2 −4x+4} + 3{y2 −6y+9}=K
    Or, 2(x −2)2 + 3(y −3)2 =K.
    From the above equation it is clear that if K >0 then the given equation will represent an ellipse and for K <0, no geometrical interpretation.
    Also if K=0 then the given equation will be reduced to a point and the point will be (2,3).

  • Question 4
    2 / -0.83

    The locus of a variable point whose distance from the point (2, 0) is  2/3  times its distance from the line x = 9/2  is

    Solution

  • Question 5
    2 / -0.83

    The axis of the parabola  9y2 −16x −12y −57 = 0 is

  • Question 6
    2 / -0.83

    A and B are two distinct points, Locus of a point P satisfying  |PA| + |PB| = 2k, a constant is

  • Question 7
    2 / -0.83

    The eccentricity of the hyperbola  x2 −y2 = 9 is

  • Question 8
    2 / -0.83

    Locus of the point of intersection of the lines x = sec  θ+ tan  θ and y = sec  θ –tan  θ is

  • Question 9
    2 / -0.83

    The line y = m x + c, touches the parabola  y2 = 4ax if

  • Question 10
    2 / -0.83

    The equations  x = at2 , y = 4at ; t ∈R  represent

  • Question 11
    2 / -0.83

     t  ∈R represents

    Solution

    P(x,y) = [(et + e-t )/2 , (et - e-t )/2]
    (et + e-t )/2 = x --------------------------(1)
    (et   - e-t )/2 = y --------------------------(2)
    Adding (1) &(2)
    2et   = 2x + 2y
    et = x + y
    Eq (1) et + e-t = 2x
    et + 1/et = 2x
    (et )2 + 1 = 2x*et
    (x+y)2 + 1 = 2x(x+y)
    x2 + y2 + 2xy + 1 = 2x2 + 2xy
    x2 + y2 + 1 = 2x2
    (x2 )/(1)2 - (y2 )/(1)2 = 1  {which represents hyperbola equation} 

  • Question 12
    2 / -0.83

    The vertex of the parabola  y2  = 4a(x −a) is

  • Question 13
    2 / -0.83

    The two parabolas  x2  = 4y and  y2  = 4x meet in two distinct points. One of these is the origin and the other is

  • Question 14
    2 / -0.83

    The equation of the directrix of the parabola  x2  = −4ay is

  • Question 15
    2 / -0.83

    The eccentricity ‘e ’of a parabola is

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