   Chapter 10.1, Problem 44E

Chapter
Section
Textbook Problem

(a) Find parametric equations for the set of all points P as shown in the figure such that |OP| = |AB|. (This curve is called the cissoid of Diodes after the Greek scholar Diodes, 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. (a)

To determine

To find: The parametric equations. of all the set of points P .

Explanation

Given:

The curve Cissoid of Diocles is shown in below figure1.

Calculation:

Let θ be the angle of inclination of segment OP .

OB=2acosθ

The point of C be (2a,0) .

The right triangle OAC .

OA=2acosθ

OP=ABOP=OBOA

Substitute (2acosθ) for |OA| and (2acosθ) for |OB| in above equation

(b)

To determine

To plot: The curve using the parametric equations. x=2asin2θ and y=2asin2θtanθ .

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