Parabola reconstruction and applications

Apply parabola geometry to reconstruction and reflector design in this precalculus practice set. Convert general equations to standard form, recover missing parameters, and use supplied dimensions to model a parabolic dish. Single-select and multiselect problems emphasize coordinate choices, diameter versus radius, focal placement, scaling and realistic aperture restrictions. Detailed explanations show the algebra and check every result against the original data. Reflector applications assume an ideal parabolic cross-section; no reflection-law proof or tangent calculus is required.