SOLUTION: The graph of |x|+|2y|=c where c>0 meets the ellipse x^2+ 4y^2 =16 in exactly 4 points. Determine the area of the convex quadrilateral with these four points as vertices.
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-> SOLUTION: The graph of |x|+|2y|=c where c>0 meets the ellipse x^2+ 4y^2 =16 in exactly 4 points. Determine the area of the convex quadrilateral with these four points as vertices.
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Question 1055387: The graph of |x|+|2y|=c where c>0 meets the ellipse x^2+ 4y^2 =16 in exactly 4 points. Determine the area of the convex quadrilateral with these four points as vertices. Answer by Fombitz(32388) (Show Source):
You can put this solution on YOUR website! .
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.Plotting the graph of the ellipse and the function shows that if the four lines lie within the ellipse and does not intersect the ellipse. If , the lines also do not intersect the ellipse. For , the lines intersect the ellipse in 8 points. The only value where there are 4 points of intersection is
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At that point, it's the sum of 4 triangle areas with a base of 4 and height of 2,
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