1. Consider the following. Eliminate the parameter to find a Cartesian equation

Question

1. Consider the following.

Eliminate the parameter to find a Cartesian equation of the curve.

2The parametric equations below describe the line segment that joins the points P1(x1,y1) andP2(x2,y2). Find parametric equations to represent the line segment from (-4, 7) to (3, -3).

x = ln t y = t t ? 64 Consider the following. Eliminate the parameter to find a Cartesian equation of the curve. The parametric equations below describe the line segment that joins the points P1(x1,y1) andP2(x2,y2). Find parametric equations to represent the line segment from (-4, 7) to (3, -3). x = x1 + (x2 - x1)t y = y1 + (y2 - y1)t Consider the following. x = 6 cos(?) y = 7 sin(?)Eliminate the parameter to find a Cartesian equation of the curve. Sketch the curve and indicate with an arrow the direction in which the curve is traced as the parameter increases. (Do this on paper. Your instructor may ask you to turn in this work.) Select the curve generated by the parametric equations. x = 3cos(t) y = t - cos(t) Consider the following. x = sin(?) y = cos(?)Eliminate the parameter to find a Cartesian equation of the curve. Sketch the curve and indicate with an arrow the direction in which the curve is traced as the parameter increases. (Do this on paper. Your instructor may ask you to turn in this work.) Consider the following. Eliminate the parameter to find a Cartesian equation of the curve. (In the restriction round the answer to two decimal places.) Sketch the curve and indicate with an arrow the direction in which the curve is traced as the parameter increases. (Do this on paper. Your instructor may ask you to turn in this work.) Select the curve generated by the parametric equations. x = 2sin(t)Describe the motion of a particle with position (x, y) as t varies in the given interval. x = 2 + 2cos(t) y = 2 + 2sin(t)If a = 4 and b = 3, find parametric equations for the curve that consists of all possible positions of the point P in the figure, using the angle ? as the parameter. The line segment AB is tangent to the larger circle.

Explanation / Answer

x = t + ln t, ... y = t - ln t

dy/dt = 1 - (1/ t ) = (t-1) / t

dx/dt = 1 + (1/ t ) = ( t + 1 ) / t .......... (1)
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dy/dx = ( dy/dt ) / ( dx/dt )

. . . . . = [ (t-1) / t ] / [ (t+1) / t ]

. . . . . = ( t - 1 ) / ( t + 1 ) ................... (2)
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... d

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