A furniture maker has a rectangular block of wood that measures 37.5 inches by 25 inches. He wants to cut it to make the largest elliptical table top possible. Find an equation of the ellipse he can use, placing the center at the origin and the major axis on the x-axis. Locate the approximate foci of the ellipse.

The largest ellipse that will fit in that table will be:

(x/(37.5/2))^2+(y/(25/2))^2=1

(x/18.75)^2+(y/12.5)^2=1

The foci will be at:

±c^2=a^2-b^2

±c^2=(18.75)^2-(12.5)^2

±c^2=195.3125

±c≈13.975

So the foci will be at approximately (-14,0) and (14,0)

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shubhamchouhanvrVT shubhamchouhanvrVT · Answer 2 · 2022-04-26T12:34:16+02:00

The focus of the elliptical table obtained from the rectangular block will be approximately (-14,0) and (14,0)

What is an ellipse?

A regular oval shape, traced by a point moving in a plane so that the sum of its distances from two other points (the foci) is constant, or resulting when a cone is cut by an oblique plane which does not intersect the base.

The largest ellipse that will fit in that table will be:

[tex](\dfrac{x}{\dfrac{37.5}{2}})^2+(\dfrac{y}{\dfrac{25}{2}})^2=1[/tex]

[tex](\dfrac{x}{18.75})^2+(\dfrac{y}{12.5})^2=1[/tex]

The foci will be at:

[tex]\pm c^2=a^2-b^2[/tex]

[tex]\pm c^2=(18.75)^2-(12.5)^2[/tex]

[tex]\pm c^2=195.3125[/tex]

±c≈13.975

So the foci will be at approximately (-14,0) and (14,0)

To know more about an Ellipse follow

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