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D. S_D9
Posted: 2023-11-20 12:13:29 Solutions will be accepted throughFor convenience, since segment A C is divided into four equal parts, we introduce coordinates scaled so that A C = 4 . We place the origin at the center of the (semi)ellipse, which is to say the midpoint between the foci F and G . Thus the equation of the ellipse will have the…
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D15. Eccentric Repulsion
Posted: 2023-11-15 19:37:25Paul is back with another elliptical quandary. Suppose you are constrained to a circular track, which we will model as the unit circle in the plane, and there is something smelly at one point on the track, say where it intersects the x -axis at the point ( 1 , 0 ) . If you…
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D9. Semi Inellipse
Posted: 2022-09-15 09:27:41PMP participant Paul Morton has also investigated the properties of ellipses. As shown in Figure 1, semiellipse C T I is inscribed in right triangle C B A so that it is tangent to hypotenuse A B at T , and so that points I and the two foci F and G of the ellipse…