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) consider $(y+2)=3(x-1)$
or, $y=3x-5$
Hence, the parametric equations becomes: $x=t; y=3t-5; -\infty \lt t \lt \infty$
(b) consider $x-1=(3) \cos t; (y+2)=(3) \sin t $
Hence, the parametric equations becomes: $x=3\cos t+1; y=3\sin t-2; 0 \leq t \leq 2 \pi$
(c) consider $y=(4x^2-x) $
Hence, the parametric equations becomes: $x=t; y=4t^2-t; -\infty \lt t \lt \infty$
(d) consider $(\dfrac{x^2}{4})+(\dfrac{y^2}{9})=1 $
Hence, the parametric equations becomes: $x=2 \cos t; y=3 \sin t; 0\leq t \leq 2 \pi$
