question archive A house builder is installing a picture window that is topped with an arch in the shape of a semi-ellipse
A house builder is installing a picture window that is topped with an arch in the shape of a semi-ellipse
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A house builder is installing a picture window that is topped with an arch in the shape of a semi-ellipse. The width is 7 feet, and the height is 3 feet. To help sketch the arch above the window, the builder uses a string attached to two thumbtacks. Approximately where (how far from the center) should the thumbtacks be placed? (Hint: it's asking you to find the foci).
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Answer:
a: semi-major axis
b: semi-minor axis.
c: distance from a focus to the center.
a= 3,5 feet; b= 1,5 feet
The following Pythagorean relationship is fulfilled:
?a2=b2+c2?
?→? ?3,52=1,52+c2?
?→? 12,25 = 2,25 ?+c2?
?→? ?c2=12,25−2,25?
?→? ?c2=10?
?→? ?c= under root10??
?→? ?c=3,16? feet at this distance is each focus from the center.
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