You are a design technician reviewing blueprints for an elliptical archway in a new corporate office building. The archway's shape is modeled by the equation $\frac{(x-3)^2}{9} + \frac{(y-1)^2}{4} = 1$. Based on this equation, what are the coordinates of the center, and what is the orientation of the major axis?

A landscape architect is designing an elliptical garden bed modeled by the equation $\frac{(x-3)^2}{9} + \frac{(y-1)^2}{4} = 1$. Match each geometric specification of the garden with its correct value or description based on this equation.

A technical illustrator is drafting an elliptical component for a machinery blueprint based on the equation $\frac{(x-3)^2}{9} + \frac{(y-1)^2}{4} = 1$. Arrange the following steps in the correct order to accurately graph the boundaries of this component on a coordinate grid.

An industrial designer is drafting a template for an elliptical machine component defined by the equation $\frac{(x-3)^2}{9} + \frac{(y-1)^2}{4} = 1$. True or False: Based on this equation, the designer can locate the vertices by starting at the center point (3, 1) and moving 3 units horizontally to the left and to the right.

Vertical Dimensions for an Elliptical Tabletop Inset

A metal fabrication apprentice is programming a CNC router to cut an elliptical opening for a customized control panel cover. The engineering blueprint defines the boundary of the elliptical cut using the standard equation: $\frac{(x-3)^2}{9} + \frac{(y-1)^2}{4} = 1$

To verify the setup on the coordinate control system, the apprentice needs to determine the horizontal distance from the center of the ellipse to its vertices (represented by $a$). According to the given equation, the horizontal distance from the center of the ellipse to its vertices is ____ units.

Drafting a Memo on Elliptical Window Coordinates