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?
***
Equation of ellipse with horizontal major axis and center at (0,0)
{{{x^2/a^2+y^2/b^2=1}}}
For given problem:
a=25
a^2=625
b=20
b^2=400
Equation: 
{{{x^2/625+y^2/400=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
..
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