SOLUTION: an elliptical window is 24 inches wide at its widest point and 12 inches tall at its tallest point. it has an elliptical frame that is 2 inches wide. what is the equation for the e

Question 545230: an elliptical window is 24 inches wide at its widest point and 12 inches tall at its tallest point. it has an elliptical frame that is 2 inches wide. what is the equation for the ellipse formed by the inside of the frame?please need help for math class.
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
The way I see it, there is the ellipse formed by the hole in the wall, with a smaller ellipse inside, at the visible edge of the glass. In between them there is a frame that is 2 inches wide.
That makes the visible part of the glass 8 inches tall (12-2-2) and 20 inches wide (24-2-2). Those are the minor and major axes of the ellipse. The equation will involve the semi-axes (half of 8 and 20, meaning 4 and 10).
The equation for an ellipse centered at the origin, can be written as
, where a and b are the semi-axes in the x and y directions
If we put the origin of our system of coordinates at the very center of the glass, with x for horizontal coordinate, and y for vertical coordinate, the edge of the glass will have the equation
<-->
At the tallest point , the edge of the glass will be at
<--><--> y=-4 and y=4 (8 inches tall).
At the widest point , the edge of the glass will be at
<--><--> x=-10 and x=10 (20 inches wide).
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