Construction and Equations
Let the radius of C be a. By translation and rotation, we may take O to be the origin and the center of the circle to be (a, 0), so A is (2a, 0). Then the polar equations of L and C are:
- .
By construction, the distance from the origin to a point on the cissoid is equal the difference between the distances between the origin and the corresponding points on L and C. In other words, the polar equation of the cissoid is
- .
Applying some trigonometric identities, this is equivalent to
- .
Let in the above equation. Then
are parametric equations for the cissoid.
Converting the polar form to Cartesian coordinates produces
Read more about this topic: Cissoid Of Diocles
Famous quotes containing the word construction:
“No construction stiff working overtime takes more stress and straining than we did just to stay high.”
—Gus Van Sant, U.S. screenwriter and director, and Dan Yost. Bob Hughes (Matt Dillon)