How to Graph an Ellipse with Center $(0, 0)$

How to Find the Equation of an Ellipse with Center $(0, 0)$ from its Graph

Standard Form of the Equation of an Ellipse with Center $(h, k)$

An architect is designing an elliptical fountain for a corporate courtyard. The fountain is centered at the origin $(0, 0)$ on the site plan, and its perimeter follows the standard equation $\frac{x^2}{a^2} + \frac{y^2}{b^2} = {}1$. Match each algebraic component from the equation to the geometric feature it describes for the fountain.

A landscape architect is designing an elliptical park area centered at the origin $(0, 0)$ on a site plan. The boundary of the park is defined by the equation $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$. If the architect wants the park's major axis to be horizontal (lying along the $x$-axis), which of the following conditions must be true?

A graphic designer is creating an elliptical company logo that is centered at the origin $(0, 0)$ on a digital canvas. The boundary of the logo is defined by the standard equation $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$. True or False: According to this standard form, the $y$-intercepts of the logo are located at the coordinates $(b, 0)$ and $(-b, 0)$.

A graphic designer is creating an elliptical logo centered at the origin $(0, 0)$ on a digital coordinate system. The logo's boundary follows the standard equation $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$. If the designer sets the parameters such that the value of $b$ is greater than the value of $a$ ($b > a$), the major axis of the logo will have a ____ orientation.

Identifying Intercepts of an Elliptical CAD Component