Constraining a Point Proportionally Along a Curve

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A point proportion t along a curve is defined variously for different types of curves as follows:

For a line segment AB, it defines the point (1t) A + tB
For a circle it defines the point on the circle which subtends angle t at the center.
For a locus or envelope, it defines the point at parameter value t.
1.Select ebd_Ebd124 a point and one of the curves mentioned above.
2.Click the Point Proportional... icon ebd_Ebd125 from the Constrain toolbox, or select Point Proportional... from the Constrain menu.
3.Enter the parameter or quantity (symbolic or real) in the data entry box.

For example, in the following diagram, D is defined proportion t along AB, and E is defined proportion t along BC. The curve is the locus of F as t varies between 0 and 1.

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In the following example, the curve is the locus of the point (x,x2). Tangents are created at points with parameter values x0 and x1 on this curve.

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