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Math Help - Ellipse problem

  1. #1
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    Ellipse problem

    How will u find out that if the point (\alpha, \beta) is outside, on or inside the ellipse \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 ?

    Hence show that the triangle whose verities are (1,2), (3,-11) and (-2,1) lies wholly inside the ellipse x^2 + 2y^2 = 13.
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  2. #2
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    Quote Originally Posted by thanapa View Post
    How will u find out that if the point (\alpha, \beta) is outside, on or inside the ellipse \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 ?

    Hence show that the triangle whose verities are (1,2), (3,-11) and (-2,1) lies wholly inside the ellipse x^2 + 2y^2 = 13.
    This entire problem can be solved by graphing.
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  3. #3
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    Quote Originally Posted by Prove It View Post
    This entire problem can be solved by graphing.
    but i need some steps ..if u could provide any
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  4. #4
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    Quote Originally Posted by thanapa View Post
    but i need some steps ..if u could provide any
    Look at the standard form equation of the ellipse: \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1

    if the constant a>b it represents the length of the major axis, and if a<b it represents the minor axis. The same thing applies to "b".

    You can now sketch the ellipse. But you can also check this without drawing a graph, if you have studied the quadratic forms.
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  5. #5
    Senior Member Shanks's Avatar
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    substitute (x,y) with (\alpha,\beta), If the value is less than 1, then inside; equal to 1, lie on the curve; is greater than 1, outside.
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