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

Answer:

$\frac{x^2}{14^2} +\frac{y^2}{10^2} =1$

Step-by-step explanation:

Given is the equation of an ellipse in standard form.

Centre is at the origin.

So ellipse would have equation as

$\frac{x^2}{a^2} +\frac{y^2}{b^2} =1$

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

$\frac{x^2}{14^2} +\frac{y^2}{10^2} =1$

Answer 2

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