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elipses 5

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An elliptical riding path is to be built on a rectangular piece of property as shown below. 

A vertical ellipse is shown centered on the coordinate plane, surrounded by a rectangle of equal length and width.

The rectangular piece of property measures 10 mi by 4 mi. Find an equation for the ellipse if the path is to touch the center of the property line on all 4 sides.

asked Aug 2, 2014 in CALCULUS by Tdog79 Pupil

1 Answer

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An elliptical riding path is to be built rectangular piece of property.

The rectangular piece of property measures 10 mi by 4 mi.

Given it is vertical ellipse.

Standard form of verrtical ellipse is image

image

a = length of semi major axis , b = length of semi minor axis.

In this case length of major axis (2a) = 10 mi

a = 5 mi

length of minor axis (2b) = 4 mi

b = 2 mi

The vertical ellipse centerd at coordinate plane.

So (h, k) = (0, 0)

Substitute a = 5, b = 2 and (h,k) = (0,0) in above standardform.

image

Equation of ellipse is image.

answered Aug 2, 2014 by david Expert

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