Ellipse

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  • Q1

    The equation of the ellipse with focus at (±5, 0) and x = 36/5 as one directrix is

    Marks:1
    Answer:

    Explanation:

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  • Q2

    The length of the semi-latus rectum of an ellipse is one third of its major axis, its eccentricity is

    Marks:1
    Answer:

    Explanation:

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  • Q3

    The eccentricity of the ellipse 25x 2 + 9y2 = 225 is

    Marks:1
    Answer:

    4/5.

    Explanation:

    The given equation is 25x2 + 9y2 = 225

    x2/9 + y2/25 = 1.

    Comparing with standard equation we get
    a = 3, b = 5,

    For ellipse,
    a = b(1 - e2)

    3 = 5(1 - e2)
    e2 = 1 - (9/25)
    e = 4/5.

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  • Q4

    The eccentricity of the ellipse 9x2 + 5y2 – 30y = 0 is

    Marks:1
    Answer:

    2/3.

    Explanation:

    The given equation can be written as

    9x2 + 5(y – 3)2 = 45 (x - 0)2/5 + (y - 3)2/9 = 1

     

    Hence, a2 = 5, b2 = 9 and the eccentricity is given by

     

    a2 = b2 (1 – e222)

     

    5 = 9(1– e2)

    Therefore, e = 2/3.

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  • Q5

    The eccentricity of an ellipse whose latus rectum is equal to distance between foci is

    Marks:1
    Answer:

    Explanation:

     The length of latus rectum of an ellipse   is 2b2/a and

     distance between foci is 2ae, where e is ecentricity of the ellipse.

            2ae = 2b2/a  (given )

         e = b2/a2         

    Also, we know that  
                 e2 = 1- b2/a2  

                 e2 = 1- e

          e2 + e -1 = 0

                        

                        

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