Calculating The Vertex Of a Square That Circumscribed EllipseHow can I find the vertex of a square that circumscribed the ellipse x 2 9 + y 2 = 1?I tried to mark the vertex at (u,v), (-u,v), (u,-v), (-u,-v) and use the equation to calculate the tangent lines to the ellipse by the vertex points, but I don't know how to continue.

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Calculating The Vertex Of a Square That Circumscribed EllipseHow can I find the vertex of a square that circumscribed the ellipse             x      2        9    +      y    2    =  1?I tried to mark the vertex at (u,v), (-u,v), (u,-v), (-u,-v) and use the equation to calculate the tangent lines to the ellipse by the vertex points, but I don&#039;t know how to continue.

levraijournalk1o · Accepted Answer

Step 1It is possible to give a very quick answer if we use this nice property of the ellipse:The locus of the intersections of perpendicular tangents to an ellipse is a circle called director circle, and the square of its radius is the sum of the squares of the ellipse semi-axes.Tangents drawn from any point on the director circle, and from its reflection about the center, form then the sides of a circumscribed rectangle. If we choose those points as the intersections between director circle and axes of the ellipse, the rectangle is by symmetry a square.Step 2In your particular case the vertices of the circumscribed square lie then at points   (  0  ,  ±      10    ) and   (  ±      10    ,  0  ).

Find the vertex of a square that circumscribed the ellipse x^2/9+y^2=1?

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