Sketch the graph of the ellipse \(\ds \frac{x^2}{9}+\frac{y^2}{16}=1\) and determine its foci. Let \(C\) be the conic which consists of all points \(P=(x,y)\) such ...

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The outer shape is an ellipse with two extra dissimilar conical sections that appear to be a parabola and a hyperbola ... end of the ellipse. Conics were described by Appolonius of Perga (c200BCE).