Question

Write an equation of an ellipse in standard form with the center at the origin and a height of 20 ft. and width of 28 ft.

Answer 1

The standard equation of an ellipse is:

(x/h)^2+(y/k)^2=1 where h and k are the radii of the x and y axis...so

(x/14)^2+(y/10)^2=1 or if you prefer

x^2/196+y^2/100=1

Answer 2

`(x^2)/(14^2) +(y^2)/(10^2) =1`

Explanation:

Given is the equation of an ellipse in standard form.

Centre is at the origin.

So ellipse would have equation as

`(x^2)/(a^2) +(y^2)/(b^2) =1`

To find a and b:

Since width is more than height this is horizontal ellipse with a>b

2a = width= 28 ft

2b = height =20 ft

a = 14 ft, b = 10 ft

`(x^2)/(14^2) +(y^2)/(10^2) =1`