Consider the cardioid as shown in the figure. Let s() be the arc length from the point

Consider the cardioid

as shown in the figure. Let s(θ) be the arc length from the point
(2, π) on the cardioid to the point (r, θ), and let p(θ) = 1/K be
the radius of curvature at the point (r, θ). Show that s and p are
related by the equation s² + 9p² = 16. (This equation is called
a natural equation for the curve.)

Transcribed Image Text:

r = 1 - cos 0, 0≤ 0 ≤ 2T