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Interested math problem

math123456

New member
Jan 16, 2019
1

Country Boy

Well-known member
MHB Math Helper
Jan 30, 2018
344
Take the original rectangle to have width "w" and height "h". Then the "reduced" ellipse has axe of length pw and ph, semi-axes pw/2 and ph/2, and is given by the equation [tex]\frac{x^2}{\left(\frac{pw}{2}\right)^2}+ \frac{y^2}{\left(\frac{ph}{2}\right)^2}= \frac{4x^2}{p^2w^2}+ \frac{4y^2}{p^2h^2}= 1[/tex].

Now, we have a rectangle Bwa by Bha that fits inside that reduced ellipse. Setting up a coordinate system with origin at the center of the ellipse, coordinate axes along the axes of the ellipse. In that coordinate system, the upper left corner of the rectangle has coordinates (Bwa/2, Bha/2) and, since that corner lies on the ellipse, must satisfy the equation of the ellipse. That is, we must have [tex]\frac{Bwa^2}{p^2w^2}+ \frac{Bha^2}{p^2h^2}= 1[/tex]