SOLUTION: an archin the form of semi ellipse is 50 ft wide at the base and its greatest height is 20ft.find its height at a distance of 10ft from the centre of the base and its width at a he

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: an archin the form of semi ellipse is 50 ft wide at the base and its greatest height is 20ft.find its height at a distance of 10ft from the centre of the base and its width at a he      Log On


   

Question 751050: an archin the form of semi ellipse is 50 ft wide at the base and its greatest height is 20ft.find its height at a distance of 10ft from the centre of the base and its width at a height of 10ft from the base?
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an archin the form of semi ellipse is 50 ft wide at the base and its greatest height is 20ft.find its height at a distance of 10ft from the centre of the base and its width at a height of 10ft from the base?
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Equation of ellipse with horizontal major axis and center at (0,0)
x%5E2%2Fa%5E2%2By%5E2%2Fb%5E2=1
For given problem:
a=25
a^2=625
b=20
b^2=400
Equation:
x%5E2%2F625%2By%5E2%2F400=1
..
find height 10 ft from center of base: (10,y)
100/625+y^2/400=1
y^2/400=1-100/625=0.84
y^2=0.84*400=336
y=±√336=±18.34
height at a distance of 10ft from the centre of the base≈18.34 ft
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find width at height 10 ft from base (x,10)
x^2/625+100/400=1
x^2/625=1-100/400=0.75
x^2=0.75*625=468.75
x=±√468.75=±21.65
width at height 10 ft from base=2*21.65≈43.3 ft