Parametric Equations

Parametric Equations Problem Solving


The line segment connecting two points (5,9)(-5, 9) and (3,2)(3, -2) can be expressed in parametric equations as x=a+bt,y=cdt.(0t1),x=-a+bt, y=c-dt. \quad (0 \leq t \leq 1),

where t=0 t=0 corresponds to the point (5,9)(-5, 9). What is the value of a+b+c+da+b+c+d?

Let aπa\pi be the area of the region bounded by the curve defined by the parametric equations x=7cos3t,y=7sin3t,x=7\cos 3t, \quad y=7\sin 3t, where 0t2π0 \leq t \leq 2\pi. What is the value of aa?

If (a,0)(a, 0) is the intersection point of the positive part of the xx-axis and the curve defined by the parametric equations x=sin4t,y=6cos8t(0t2π),x=\sin 4t, y=6\cos 8t \quad (0 \leq t \leq 2\pi), what is the value of 1a4?\frac{1}{a^4}?.

What is the polar equation of this graph?

Two clowns, Twinkle and Jingle, are throwing pies at each other. Twinkle throws a pie toward Jingle from 500 500 centimeters away. Its flight path is given by parametric equations {x=100ty=80t16t2 \begin{cases} x &=& 100t \\ y &=& 80t - 16t^2 \end{cases} where tt is time in seconds.

Two seconds later Jingle launches an interceptor pie from his location with the flight path {x=500500(t2)y=K(t2)16(t2)2 \begin{cases} x &=& 500 - 500(t-2) \\ y &=& K(t-2) - 16(t-2)^2 \end{cases} Find the value of KK which will guarantee that the interceptor pie will hit its target (the pie thrown by Twinkle).


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