Question

The parametric equations x = square root t, y= 3t - 4 for t in [ 0,4] define a plane curve

Answer 1

Answer:

a) We kindly invite you to read the explanation and check the image attached below for further details.

b) The rectangular equation is $y = 3\cdot x^{2}-4$.

Step-by-step explanation:

a) Let $x = \sqrt{t}$ and $y = 3\cdot t -4$ for $t\in[0,4]$. We proceed to graph the expression with the help of a graphing tool. In this case, the tool Desmos is used and the result is presented below.

b) The rectangular equation for the curve is:

$t = x^{2}$ (1)

$y = 3\cdot t - 4$ (2)

By applying (1) in (2), we get the following equation in rectangular form:

$y = 3\cdot x^{2}-4$