Answer
a) $x=t; y=3t-5; -\infty \lt t \lt \infty$
b) $x=3\cos t+1; y=3\sin t-2; 0 \leq t \leq 2 \pi$
c) $x=t; y=4t^2-t; -\infty \lt t \lt \infty$
d) $x=2 \cos t; y=3 \sin t; 0\leq t \leq 2 \pi$
Work Step by Step
a) Here, $y+2=3(x-1) \implies y=3x-5$
Thus, the parametric equations are: $x=t; y=3t-5; -\infty \lt t \lt \infty$
b) Here, $x-1=3 \cos t,y+2=3 \sin t $
Thus, the parametric equations are: $x=3\cos t+1; y=3\sin t-2; 0 \leq t \leq 2 \pi$
c) Here, $y=4x^2-x $
Thus, the parametric equations are: $x=t; y=4t^2-t; -\infty \lt t \lt \infty$
d) Here, $\dfrac{x^2}{4}+\dfrac{y^2}{9}=1 $
Thus, the parametric equations are: $x=2 \cos t; y=3 \sin t; 0\leq t \leq 2 \pi$
