Finding a Polar Equation Determine the polar equation of the set of all points , the product of whose distances from the points and is equal to 1, as shown in the figure.
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Finding a Polar Equation Four dogs are located at the corners of a square with sides of length d. The dogs all move counterclockwise at the same speed directly toward the next dog, as shown in the figure. Find the polar equation of a dog’'s path as it spirals toward the center of the square.
Lemniscate Let and be the distances from the point to the points and , respectively, as shown in the figure. Show that the equation of the graph of all points satisfying is
This curve is called a lemniscate. Graph the lemniscate and identify three points on the graph.
Cissoid of Diocles Consider a circle of radius a tangent to the y-axis and the line , as shown in the figure. Let A be the point where the segment OB intersects the circle, where point B lies on the line . The cisoid of Diocles consists of all points P such that .
(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.
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