Question
(a) Find parametric equations for the set of all points $ P $ as shown in the figure such taht $ | OP | = | AB | $. (This curve is called the cissoid of Diocles after the Greek scholar Diocles, who introduced the cissoid as a graphical method for constructing the edge of a cube whose volume is twice that of a given cube.)(b) Use the geometric description of the curve to draw a rough sketch of the curve by hand. Check your work by using the parametric equations to graph the curve.
Step 1
From the given figure, we can see that OP is the hypotenuse of a right triangle with sides OA and AP. Using the Pythagorean theorem, we can find that the length of OP is $\sqrt{OA^2 + AP^2}$. Show more…
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$$ \begin{array}{l}{\text { (a) Find parametric equations for the set of all points } P \text { as }} \\ {\text { shown in the figure such that }|O P|=|A B| \text { . (This curve }} \\ {\text { is called the cissoid of Diocles after the Greek scholar }} \\ {\text { Diocles, who introduced the cissoid as a graphical }} \\ {\text { method for constructing the edge of a cube whose volume }}\end{array} $$ $$ \begin{array}{l}{\text { is twice that of a given cube.) }} \\ {\text { (b) Use the geometric description of the curve to draw a }} \\ {\text { rough sketch of the curve by hand. Check your work by }} \\ {\text { using the parametric equations to graph the curve. }}\end{array} $$
Parametric Equations and Polar Coordinates
Curves Defined by Parametric Equations
(a) Find parametric equations for the set of all points $P$ as shown in the figure such that $|O P|=|A B| .$ (This curve is called the cissoid of Diocles after the Greek scholar Diocles, who introduced the cissoid as a graphical method for constructing the edge of a cube whose volume is twice that of a given cube.) (b) Use the geometric description of the curve to draw a rough sketch of the curve by hand. Check your work by using the parametric equations to graph the curve.
Find parametric equations for the set of all points P as shown in the figure, where a = 4, such that |OP| = |AB|. (This curve is called the cissoid of Diocles after the Greek scholar Diocles, who introduced the cissoid as a graphical method for constructing the edge of a cube whose volume is twice that of a given cube. Enter your answer as a comma-separated list of equations. Let x and y be in terms of ̘.)
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