In Exercises 21-40, eliminate the parameter t. Then use the rectangular equation to sketch the plane curve represented by the given parametric equations. Use arrows to show the orientation of the curve corresponding to increasing values oft. (If an interval for t is not specified, assume that
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- Sketch and describe the orientation of the curve given by the parametric equations x=2tandy=4t2+2,2t2.arrow_forwardShow that the graph of the parametric equations x = a + (c − a)t, y = b+(d−b)t, t ∈ [0, 1] is a line segment from (a, b) to (c, d ).arrow_forwardFind the length of the curve r = 2 sin^3 (u/3), 0 … u … 3pi , in the polar coordinate plane.arrow_forward
- Eliminate the parameter t from the parametric equations x = 3 cos t, y = 5 sin t and then sketch the graph of the plane curve.arrow_forwardFind the parametric equation of the line passing through the points P = (1, 2, −1) and Q = (1, −1, −2).arrow_forwardFind the length of the curve r = 2 sin^3 (u/3), 0<=u<=3pai, in the polar coordinate plane.arrow_forward
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- Suppose a parametric equations for the line segment between (5,2) and (7,8) have the form: x(t)= a+bt y(t)= c+dt If the parametric curve starts at (5,2) when t=0 and ends at (7,8) at t=1, then find a,b,c, and darrow_forward9.1.2 Sketch the plane curve defined by the given parametric equations, and find an x-y equation for the curve. x=1+2cos(t) y=-2+2sin(t)arrow_forwardThe parametric equation for the line passing through P(1,1,5) and parallel to n=(0,0,1) is defined as a, x = 1, y = 1, z = -5 + t b. x = 1, y = 1, z = 5 + t c. x = 1, y = -1, z = 5 + t d. x = 1, y = 1, z = 5 - tarrow_forward
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