JEE Main: Co-ordinate Geometry Exam Quiz!

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| By Tanmay Shankar
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Tanmay Shankar
Community Contributor
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JEE Main: Co-ordinate Geometry Exam Quiz! - Quiz

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Questions and Answers
  • 1. 

    If the line x = 1/2, is the directrix of a parabola y2 – kx + 6 = 0, then which of the following is a value of ‘k’?  

    • A.

      – 4

    • B.

      – 6

    • C.

      – 1/4

    • D.

      – 8

    Correct Answer
    B. – 6
  • 2. 

    Equations x = t2+t+1 and y = t2 – t +1, represents which of the following curve?

    • A.

      An ellipse

    • B.

      A pair of straight

    • C.

      A hyperbola

    • D.

      A parabola

    Correct Answer
    D. A parabola
  • 3. 

    Angle between tangents drawn from the point (2, 1) to the parabola y2 = – 32x is:

    Correct Answer
    B.
  • 4. 

    A parabola has the origin at it focus and the line x = 2 as its directrix. Then the vertex of the parabola will be at: 

    • A.

      (2, 0)

    • B.

      (0, 2)

    • C.

      (1, 0)

    • D.

      (0, 1)

    Correct Answer
    C. (1, 0)
    Explanation
    from the diagram it is clear that the vertex will be the midpoint of OP So co-ordinate of vertex are (1, 0)

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  • 5. 

    The eccentricity of the ellipse with its centre at the origin is 1/2. If one of the directrix is x = 4, then which of the following correctly represent the equation of ellipse. 

    Correct Answer
    A.
  • 6. 

    The number of values of c such that the straight line y = 4x + c touches the curve ;is:

    • A.

      4

    • B.

      0

    • C.

      Infinite

    • D.

      2

    Correct Answer
    D. 2
  • 7. 

    Tangents are drawn to the ellipse at the end of the latus retum. The area of the quadrilateral so formed is: 

    • A.

      54

    • B.

      27

    • C.

      27/2

    • D.

      36

    Correct Answer
    A. 54
  • 8. 

    If x = 9 is the chord of the contact of the hyperbola x2 – y2 = 9, then the equation of the corresponding pair of tangents is 

    Correct Answer
    B.
  • 9. 

    2x + √6 y = 2 touches the hyperbola x2 – 2y2 = 4, then the point of contact is: 

    • A.
    • B.
    • C.

      Both a & b

    • D.

      None of these

    Correct Answer
    C. Both a & b
  • 10. 

    The eccentricity of hyperbola 3x2 – y2 = 4 is: 

    • A.

      1

    • B.

      5

    • C.

      – 2

    • D.

      2

    Correct Answer
    D. 2

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  • Current Version
  • Mar 21, 2023
    Quiz Edited by
    ProProfs Editorial Team
  • Aug 27, 2014
    Quiz Created by
    Tanmay Shankar
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