elipses 5

Question

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



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.

Answer 1

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

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.

Equation of ellipse is .