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

Documenting Elliptical Dimensions for Quality Control

A design technician at a custom woodworking shop is drafting a blueprint for an elliptical conference table. On a coordinate grid centered at the origin (0, 0), the outer boundary of the table is modeled by the standard equation $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$, where the horizontal semi-major axis $a$ is greater than the vertical semi-minor axis $b$ ($a > b$). To verify the layout coordinates before sending the design to a CNC cutting machine, the technician must execute a standard analytical procedure. Arrange the following steps in the correct order to recall and identify the geometric features of the table, from extracting the initial equation constants to establishing the major axis intercepts.