Nicomedes2

Conchoid of Nicomedes

Below we describe the conchoid of Nicomedes, constructed through the [implicit function tool]. The figure depends on numbers (a) and (k), defining the corresponding parameters. It depends also from the frame ABCD, which restricts the curve. The description is created automatically by slecting the menu-item [File-Image\Describe Schemes]. Look at Nicomedes.html for a different construction of the curve, as a geometric locus.

<-- SCHEME-START -- >
<-- TOOL -- > Select the Point-tool: (3rd-Button), (Shortcut: Ctrl+E).
Click at P to define a point there.
<-- TOOL -- > Define a Formula-Object:
Type somewhere the text-box {formula (a-x)^2*(x^2+y^2)-k^2*x^2}. Then select it and press the RETURN key.
<-- TOOL -- > Select the Screen-Rectangle-tool: (9th-Button/2nd-Button from below).
Click at A, drag ... , release at C to define the screen-rectangle m = (ABCD).
<-- TOOL -- > Select the Cartesian-Coordinates-tool: (Measures-Menu\Cartesian Coordinates_ ).
Click on P in order to define the group of its Cartesian coordinates x= ..., y=... .
<-- TOOL -- > Evaluate a Formula for a list of arguments. For this:
Right-click on Formula { (a-x)^2*(x^2+y^2)-k^2*x^2} and select the menu-item {Activate}. Then click on each number of the list: { 0.40} { -0.7143} { 2.5102} { 3.1000}, getting { 3.5541}.
<-- TOOL -- > Select the tool of Implicit-Restricted-Functions: (14th-Button/last item).
Click on point P, then on the number-object { 3.5541} and finally on screenrect m in order to find all points point P (inside the rectangle) such that z({ 3.5541}) is zero.
<-- SCHEME-END -- >

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