Question 679828: A racetrack is in the shape of an ellipse, 210 feet long and 70 feet wide. what is the width 10 feet from a vertex?
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! A racetrack is in the shape of an ellipse, 210 feet long and 70 feet wide. what is the width 10 feet from a vertex?
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Standard form for an ellipse with major horizontal axis: (x-h)^2/a^2+(y-k)^2=1, a>b, (h,k)=center
For given problem:
center:=(0,0)
length of major axis=210=2a
a=105
a^2=105^2=11025
length of minor axis=70=2b
b=35
b^2=35^2=1225
equation: x^2/11025+y^2/1225=1
at 10 ft from vertex, x=105-10=95ft
solving for y:
y^2=[35^2-(35/105)^2*x^2]
=[35^2-(35/105)^2*95^2]
=[1225-(1225/11025)*9025]=[1225-1002.78]≈(222.22)
y=±√222.22≈±14.9
width of racetrack 10 feet from a vertex≈2y≈29.8 ft
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