Answer to Question #175749 in Calculus for Shahir Sheikh

Question

Match the parametric equations to the shape of their graphs.

x = 2t + 1

y = 1 - t

shape:

x = t - t²

y = 1/2(t -3)

shape:

x = cos(t)

y = sin(t)

shape:

x = t² - 1

y = sin(t)

shape:

Answer 1

1. t=(x-1)/2

y=-x/2+1.5

shape: line

2. t=2y+3

x=2y+3-4y²-9=-4y²+2y-6

shape: parabola

3.

$x^2=cos^2t=1-sin^2t$

$y^2=sin^2t$

$x^2=1-y^2$

$x^2+y^2=1$

circle

4. $t=\sqrt{x+1}$

$y=sin(\sqrt{x+1})$

shape: sinusoid, x>-1