   Chapter 10, Problem 15PS

Chapter
Section
Textbook Problem

# Cissoid of Diocles Consider a circle of radius a tangent to the y-axis and the line x = 2 a , as shown in the figure. Let A be the point where the segment OB intersects the circle, where point B lies on the line x = 2 a . The cisoid of Diocles consists of all points P such that O P = A B .(a) Find a polar equation of the cissoid.(b) Find a set of parametric equations for the cissoid that does not contain trigonometric functions.(c) Find a rectangular equation of the cissoid. Figure for 15

(a)

To determine

To calculate: The polar equation of the cissoid.

Explanation

Given: The cissoids contains the points such that for the provided figure OP=AB.

Calculation:

Consider the triangle OCB.

cosθ=2aOBOB=2asecθ

Now consider triangle OAC

(b)

To determine

To calculate: The parametric equations of the cissoids without the trigonometric functions.

(c)

To determine

To calculate: The rectangular equation of the cissoid.

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