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Math Help - ellipse problem

  1. #1
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    ellipse problem

    How will you find out 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 vertices are (1,2),(3,-1) and (-2,1) lies wholly inside the ellipse x^2+2y^2=13.
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  2. #2
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    Hello, varunnayudu!

    How will you find out if the point (\alpha,\beta) is outside, on or inside the ellipse \frac{x^2}{a^2}+\frac{y^2}{b^2}\:=\:1
    Substitute (\alpha,\beta) into the equation.
    Compare the left side to the right side.

    If the left is: . \begin{Bmatrix}\;<  & \text{inside} \\ \;=  & \text{on} \\ \;>  & \text{outside} \end{Bmatrix}




    Hence, show that the triangle whose vertices are (1,2),(3,-1) and (-2,1)
    lies wholly inside the ellipse x^2+2y^2\:=\:13
    Apply the above test to the three vertices.

    Since an ellipse is convex, if the vertices are inside the ellipse,
    . . the sides are also inside the ellipse.

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