Ellipses An ellipse is generated by the parametric equations x = a cos t, y = b sin t. If 0 < a < b, then the long axis (or major axis) lies on the y-axis and the short axis (or minor axis) lies on the x-axis. If 0 < b < a, the axes are reversed. The lengths of the axes in the x- and y-directions are 2a and 2b, respectively. Sketch the graph of the following ellipses.Specify an interval in t over which the entire curve is generated. x = 12 sin 2t, y = 3 cos 2t

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Q: Eliminate the parameter and obtain the standard form of the rectangular equation. Ellipse: x = h + a…

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Q: Eliminate the parameter and obtain the standard form of the rectangular equation. Hyperbola:  x = h…

A: x = h + b tanθ        ⇒ tanθ = x-hb —1 y = k + a secθ        ⇒ secθ = y-ka —2    22 - 12      sec2θ…

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Q: Eliminate the parameter and obtain the standard form of the rectangular equation. Ellipse: x = h + a…

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Q: Eliminate the parameter and obtain the standard form of the rectangular equation. Hyperbola: x =h +b…

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Q: 34. (a) Find a parametric representation for the torus obtained by rotating about the z-axis the…

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