Question

A pool is built in the shape of an ellipse, centered at the origin. The maximum vertical length is 30 feet, and the maximum horizontal width is 14 feet. Which of the
following equations represents the pool?

Answer 1

The equation of the ellipse is $\frac{x^{2}}{49} + \frac{y^{2}}{225} = 1$.

In this question we should read carefully the statement, find all relevant information and derive the resulting ellipse formula. Geometrically, the standard formula of the ellipse is:

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

Where:

• $x$ - Horizontal distance, in feet.
• $y$ - Vertical distance, in feet.
• $a$ - Horizontal semiaxis length, in feet.
• $b$ - Vertical semiaxis length, in feet.

If we know that $a = 7$ and $b = 15$, hence the equation of the ellipse is:

$\frac{x^{2}}{49} + \frac{y^{2}}{225} = 1$

The equation of the ellipse is $\frac{x^{2}}{49} + \frac{y^{2}}{225} = 1$.

We kindly invite to check this question on ellipses: https://brainly.com/question/14281133