Kelper gave the following construction from a hyperbola with foci at A and B and
ID: 2979176 • Letter: K
Question
Kelper gave the following construction from a hyperbola with foci at A and B and with one vertex at C: Let pins be placed at A and B. To A let a thread with length AC be tied and to B a thread with length BC. Let each thread be lengthened by an amount equal to itself. Then grasp the two threads together with one hand (starting at C and little by little move away from C, paying out the two threads. With the other hand, draw a path of the join of the two threads at the fingers. Show that the path is a hyperbola. Could someone show the work on how to get to an answer, pleaseExplanation / Answer
In mathematics, an ellipse (from Greek ???????? elleipsis, a "falling short") is a plane curve that results from the intersection of a cone by a plane in a way that produces a closed curve. Circles are special cases of ellipses, obtained when the cutting plane is orthogonal to the cone's axis. An ellipse is also the locus of all points of the plane whose distances to two fixed points add to the same constant. The name ???????? was given by Apollonius of Perga in his Conics, emphasizing the connection of the curve with "application of areas". Ellipses are closed curves and are the bounded case of the conic sections, the curves that result from the intersection of a circular cone and a plane that does not pass through its apex; the other two (open and unbounded) cases are parabolas and hyperbolas. Ellipses arise from the intersection of a right circular cylinder with a plane that is not parallel to the cylinder's main axis of symmetry. Ellipses also arise as images of a circle under parallel projection and the bounded cases of perspective projection, which are simply intersections of the projective cone with the plane of projection. It is also the simplest Lissajous figure, formed when the horizontal and vertical motions are sinusoids with the same frequency.
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