A graphic designer is creating an elliptical logo for a client's branding project. The designer is using the coordinate equation $\frac{(x-2)^2}{25} + \frac{(y+3)^2}{16} = 1$ to plot the shape accurately on a digital grid. Arrange the following steps in the correct order to graph the logo.

A machinist is programming a CNC router to cut an elliptical slot for a custom control panel. The design blueprint specifies the opening using the coordinate equation $\frac{(x-12)^2}{64} + \frac{(y+5)^2}{16} = 1$, where units are in millimeters. Match each component of the elliptical slot to its correct value or description based on this equation.

An HVAC technician is mapping out an elliptical ceiling vent on a coordinate grid for a commercial building project. The vent's shape is defined by the equation $\frac{(x+8)^2}{144} + \frac{(y-10)^2}{64} = 1$. To begin the layout, the technician must identify the center point of the ellipse. Based on the standard form equation, what are the coordinates of the center (h, k)?

A logistics coordinator is mapping an elliptical delivery zone for a warehouse drone using the coordinate equation $\frac{(x-40)^2}{144} + \frac{(y-60)^2}{100} = 1$. True or False: Based on the rules for graphing ellipses, the coordinator identifies that the major axis of this zone is horizontal because the larger denominator (144) is associated with the $x$-variable.

A team of landscape architects is drafting an elliptical layout for a corporate courtyard. They are mapping the boundary using the standard form equation, $\frac{(x-h)^2}{a^2} + \frac{(y-k)^2}{b^2} = 1$. After plotting the center point at (h, k), they need to establish the length of the major axis. To find the distance from the center to the vertices along this axis, they must recall the graphing rules and take the square root of the ____ denominator.

Determining the Orientation of an Elliptical Layout

Guide to Graphing an Ellipse with Center (h, k)