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Conic Section Test - 16

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Conic Section Test - 16
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  • Question 1
    4 / -1
    An ellipse is drawn by taking a diameter of the circle (x - 1)2 + y2 = 1 as its semi-minor axis and a diameter of the circle x2 + (y - 2)2 = 4 is semi - major axis, if the centre of the ellipse at the origin and its axis are the coordinates axes, then the equation of the ellipse is
  • Question 2
    4 / -1

  • Question 3
    4 / -1
    The line x = 2y intersects the ellipse x2/4 + y2 = 1 at the points P and Q. The equation of the circle with PQ as diameter is
  • Question 4
    4 / -1
    Let P and Q are the points on the parabola y2 = 4x, if so that the line segment PQ subtends right angle at the vertex. If PQ intersects the axis of the parabola at R, then the distance of the vertex from R is
    Solution

  • Question 5
    4 / -1
    If the eccentricity of the hyperbola x2/a2 - y2/b2 = 1 is reciprocal to that of the ellipse x2 + 4y2 = 4. If the hyperbola passes through the focus of the ellipse, then
  • Question 6
    4 / -1
    Equation of the ellipse whose axes are the axes of coordinates and which passes through the point (-3, 1) and has eccentricity √(2/5) is
  • Question 7
    4 / -1
    The circle x2 + y2 - 8x = 0 and hyperbola x2 /9 - y2/4 = 1 intersect at the points A and B.
    Equation of a common tangent with positive slope to the circle as well as to the hyperbola is
  • Question 8
    4 / -1
    The circle x2 + y2 - 8x = 0 and hyperbola x2/9 - y2/4 = 1 intersect at the points A and B.
    Equation of the circle with AB as its diameter is
  • Question 9
    4 / -1
    The ellipse x2 + 4y2 = 4 is inscribed in a rectangle aligned with the coordinate axes, which is turn in inscribed in another ellipse that passes through the point (4, 0). Then, the equation of the ellipse is
  • Question 10
    4 / -1
    Focus of hyperbola is (±3, 0) and equation of tangent is 2x + y - 4 = 0, find the equation of hyperbola is
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