[color=#000000]Recall the locus definition of a [b]parabola[/b] (illustrated [url=https://www.geogebra.org/m/BFK6P7Ac]here[/url] if you need a refresher). [br][br]Well, imagine spinning this parabola 360 degrees about its axis (of symmetry).[br]Doing so yields a 3D solid called a [/color][b][color=#bf9000]circular paraboloid of revolution. [br][br][/color][/b][color=#000000]Interact with this applet for a few minutes.[/color] [br][color=#cc0000][i]Be sure to slide the[/i][/color] [b][color=#000000]Slide Me![/color] [/b][color=#cc0000]slider completely once [/color][b][color=#000000][i]before[/i][/color][/b][color=#cc0000] messing around with the other sliders! [br][/color][color=#1e84cc][b]Note: Point P is a point that lies on this solid. Move it wherever you'd like. [br] [/b][/color]After doing so, answer the question that follows. [br][br][color=#1e84cc][b]To explore this resource in Augmented Reality, see the directions that appear below the applet. [/b][br][/color]
A circular paraboloid of revolution is a locus (set of points that satisfy a condition or set of conditions). [br]How would you describe this locus?
A [color=#000000][b]circular paraboloid of revolution[/b][/color] is a locus of point that are all equidistant [color=#000000][b]from a fixed point, called a focus,[/b][/color] and a [color=#1e84cc][b]fixed plane. [br][br][/b][/color]Note the adjective [b][color=#000000]circular[/color][/b] is used here because cross sections of this solid parallel to the [color=#1e84cc][b]fixed plane[/b][/color] are circles.
1) Open up GeoGebra 3D app on your device.[br][br]2) Go to MENU, OPEN. Under SEARCH, type [b]g3uusvay[/b][color=rgba(0, 0, 0, 0.870588235294118)].[br][br][/color]3) [b]The xcoord slider controls the x-coordinate of point P. [br] The ycoord slider controls the y-coordinate of point P.[/b][b][color=#bf9000] [br] The yellow e slider controls the opacity of the paraboloid.[br][/color][/b][b][color=#0000ff] The blue i slider controls the opacity of the (directrix) plane.[br][/color][/b][b] The a slider stretches (or compresses) the paraboloid vertically (with respect to z). [br] [br][/b][b] The slider named d provides the animation. [br][br][/b][b] Set the boolean variable [/b][b]n equal to "true" if you want to see [br] the 2d-parabola [/b][b]= cross section of the paraboloid of revolution and vertical plane containing P. [br][/b]