MAT136H1 Lecture Notes - Unit Circle, Polar Coordinate System
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Question #4 (medium): parametric equations for circle & ellipse. Given that and representing a unit circle with radius , shift of units in the - direction and units in the -direction is represented by and . This is a circle with radius centered at where. If and where then it is an ellipse centered at the origin, with radius stretch of from the origin about the -direction and stretch of radius by in the -direction. Like the circle, the center of the ellipse can shift by by being added unto the parametric equations for and . Describe the motion of a particle with position as varies in the given interval. The parametric equations are in the form of and , but notice that it is not the same radius in the and directions. Thus the equations form an ellipse, with center at .
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