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.

For those who need a written explanation:

Step-by-step explanation:

Since the ellipse is vertical, we use the equation (x^2/b^2)+(y^2/a^2)=1. a=10/2, or 5 while b=4/2, or 2. Plug these into the equation to have (x^2/2^2)+(y^2/5^2)=1. Now simplify to get: (x^2/4)+(y^2/25)=1 which is our answer.

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below:

it would be:

c.parallelogram.