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Equation of ellipse

  1. Oct 21, 2015 #1
    Find the equation of the ellipse whose eccentricity is 2/3 and which has (2,0) and x+y=0 for focus and corresponding directrix .

    given answer: (x-2)^2 + y^2 = 4/9 ( ( (x+y)/√2)^2)


    what i tried doing:-

    ae=2
    ⇒a*2/3=2
    ∴a=3

    found b=√5.

    what to do next? please help.
     
  2. jcsd
  3. Oct 21, 2015 #2

    Mark44

    Staff: Mentor

    Have you drawn a sketch of the ellipse? Based on the given information, the major axis of the ellipse is a line with slope 1 that goes through the point (2, 0). You will need to know how to write the equation of an ellipse that is not in standard orientation. The rotation is the reason for the xy term in the equation.

    Also, in future posts, please do not delete the three parts of the homework template.
     
  4. Oct 22, 2015 #3
    Thanks a lot Mark.
     
  5. Oct 22, 2015 #4

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    You started by calculating a value of some number, "a". Why? What does "a" mean? The fact that you did that must mean that you have some formula that involves "a". What is that formula?
     
  6. Oct 22, 2015 #5
    Thanks for taking interest in my thread HallsofIvy.

    'a' represents the semimajor axis of the ellipse.
    'b' represents the semiminor axis.
    e: eccentricity
    Foci : + or - ae ( since there r 2 foci.)

    I realised that finding a or b, however, was unnecessary.
     
    Last edited: Oct 22, 2015
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