37–38 Compare the curves represented by the parametric equations. How do they differ?
(a)
(b)
(c)
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Chapter 10 Solutions
Calculus (MindTap Course List)
- Epicycloid If the circle C of Exercise 63 rolls on the outside of the larger circle, the curve traced out by P is called an epicycloid. Find parametric equations for the epicycloid. Hypocycloid A circle C of radius b rolls on the inside of a larger circle of radius a centered at the origin. Let P be a fixed point on the smaller circle, with the initial position at the point (a,0) as shown in the figure. The curve traced out by P is called a hypocycloid. a Show that parametric equations of hypocycloid are x=(ab)cos+bcos(abb) y=(ab)sinbsin(abb) b If a=4b, the hypocycloid is called an asteroid. Show that in this case parametric equations can be reduced to x=acos3y=asin3 Sketch the curve. Eliminate the parameter to obtain an equation for the asteroid in rectangular coordinates.arrow_forwardx=e-t Cost y=e-t S int find the equations of the tangent and normal lines of the parametric curve at the point t=0arrow_forwardAn object moves along the curve determined by the parametric equations x(t) = t−sin(2t) and y(t) = t−cos(2t) where t is time in seconds and position is measured in meters. Find the speed of the object at time t=5/2 π seconds. A) 100 meter per second B) √10 mps C) √2 mps D) 3√2 mpsarrow_forward
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