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Mathematics Test 89
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Mathematics Test 89

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  • Question 1/10
    4 / -1

    Equation of normal to the parabola y2 = 4x which is perpendicular to the line x + 3y + 1 = 0 is :-

    Solutions

    m = 3

    y = mx – 2am – am3

    put a = 1, m = 3

    y = 3x – 6 – 27 ⇒ y = 3x – 33 ⇒ 3x – y –33 =0

    ⇒ b2 = 16

     

     

  • Question 2/10
    4 / -1

    The eccentricity of the ellipse with centre at the origin which meets the straight line  x/7 + y/2 = 1on the axis of x and the straight line   x/3 - y/5 = 1on the axis of y and whose axes lie along the axes of coordinates is-

    Solutions

     

  • Question 3/10
    4 / -1

    If the line y = 3x + λ touches the hyperbola 9x2 – 5y2 = 45, then the value of λ is-

    Solutions

    Equation of hyperbola can be written as

     x2/5 - y2/9 = 1

    & straight line y = 3x + l is a tangent of hyperbola.

    By the condition of tangency

    c2 = a2m2 - b2

    ⇒ λ2 = 5(9) – 9

    ⇒ λ2 = 36

    ⇒ λ = ±6

     

  • Question 4/10
    4 / -1

    The equation of the common tangent touching the circle (x – 3)2 + y2 = 9 and the parabola y2 = 4x above the x-axis, is :-

    Solutions

     

  • Question 5/10
    4 / -1

    If the eccentricities of the ellipse   x2/4 + y2/3= 1 and the hyperbola x2/64 - y2/b2= 1 are reciprocals of each other, then b2 =

    Solutions

     

  • Question 6/10
    4 / -1

    The product of the lengths of perpendiculars drawn from any point on the hyperbola x2 – 2y2 – 2 = 0 to its asymptotes is:-

    Solutions

     

  • Question 7/10
    4 / -1

    If the tangent at any point P on the ellipse  x2/a2 + y2/b2 = 1 meets the tangents at the vertices A and A' in L and L' respectively, then AL. A'L' =

    Solutions

     

  • Question 8/10
    4 / -1

    AB is any focal chord of parabola y2 = 8x, then length of AB can never be less than -

    Solutions

  • Question 9/10
    4 / -1

    The eccentric angles of extremities of latus rectum of ellipse x2/25 + y2/16 = 1 are given by -

    Solutions

     

  • Question 10/10
    4 / -1

    The latus rectum of the parabola whose focal chord is PSQ, such that PS = 3, QS = 2, S is focus, is given by:-

    Solutions

     

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