Question

An elliptical garden is 26 feet long and 14 feet wide. Write an equation for the shape of the garden. Then find the area of the garden. Assume the major axis is horizontal

Answer 1

Equation of shape: x^2/169 + y^2/49 = 1

Area = 285.885 ft2

Explanation:

The equation for a ellipse is:

x^2/a^2 + y^2/b^2 = 1

Where a is half of the horizontal axis and b is half of the vertical axis.

So, is the horizontal axis is 26 feet long and the vertical axis is 14 feet wide, we have that a = 13 and b = 7, so the equation for the shape of the garden is:

x^2/(13)^2 + y^2/(7)^2 = 1

x^2/169 + y^2/49 = 1

The area of the ellipse is calculated with this formula:

Area = pi * a * b

So as we have a = 13 and b = 7, we have that:

Area = pi * 13 * 7 = 285.885 ft2