3. Constructing a Point on a Cassini Oval
3. Constructing a Point on a Cassini Oval
This Demonstration shows another ruler-and-compass construction of a point on a Cassini oval.
An ellipse is given with the equation +=1 and eccentricity , . Choose any point on . Let be the point opposite and let be a point on different from and . Tangents to at and are parallel and meet the tangent at and at points and , respectively. Then .
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ϵ=-
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a≥b>0
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ℰ
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=-
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Draw a circle with center and radius and a circle with center and radius ; suppose these meet in points and . But then . Thus is a point on a Cassini oval with foci and . The same is true for the point . It can be shown that the foci and are also on the oval.
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TT=-
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T
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