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Conic Sections Test - 7

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Conic Sections Test - 7
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Weekly Quiz Competition
  • Question 1
    2 / -0.83

    The ellipse  

  • Question 2
    2 / -0.83

    The equations x = a cos  θ , y = b sin  θ, 0  ≤ θ <2 π, a  ≠ b, represent

  • Question 3
    2 / -0.83

    The graph of the function f(x) i/x i.e. the curve y = 1/x is

  • Question 4
    2 / -0.83

    The line y = c touches the parabola  y2  = 4ax  when

  • Question 5
    2 / -0.83

    The parabolas  x2  = 4y and  y2  = 4x intersect

  • Question 6
    2 / -0.83

    The lngth of the common chord of the parabolas  y2 = x and  x2  = y is

    Solution

  • Question 7
    2 / -0.83

    The number of points on X-axis which are at a distance c units (c <3) from (2, 3) is

    Solution

    Distance of 'c 'units from (2,3)
    Let the no: of points be (x,0)
    By distance formula
    {(2 −x)2 +(3 −0)2 }=c
     4 −4x+x2 +9=c
    ⇒x2 −4x+13 = c:c=2,2
    There are the points of c,such that when they are applied back to the equations,the number of points will become zero.

  • Question 8
    2 / -0.83

    The eccentricity of the conic  9x2  −16y2  = 144 is

  • Question 9
    2 / -0.83

    The eccentricity of  3x2 +4y2  = 24 is

  • Question 10
    2 / -0.83

    The angle between the tangents drawn from the origin to the circle = (x −7)2 +(y+1)2 = 25 is  

    Solution

    Let the equation of tangent drawn from (0,0) to the circle be y=mx. Then, p = a ⇒7m+1/(m2 +1)1/2 = 5
    ⇒24m2 + 14m −24=0
    ⇒12m2 + 7m −12=0
    ⇒m1m2 = −12/12 =−1
    ∴Required angle = π/2

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