Question

A catapult is malfunctioning and not throwing objects in the intended manner. The builders have modeled the path of the objects thrown by using the following parametric equations. rewrite the parametric equations by eliminating the parameter.

x(t)=2t-1
y(t)= square root of t; t> or equal to 0

Answer 1

The correct answer is:

D.
`x=2y^(2) -1, y\geq 0`

Answer 2

The equation is
`y ^ 2 = (x + 1)/(2)`

Explanation:

The parameter that we have is t. We want to eliminate this parameter in both equations, therefore in the first equation we solve for t and in the second equation we solve for the variable t.

We have:

`x = 2t-1\\\\x + 1 = 2t\\\\t = (x + 1)/(2)`

Now we solve the other equation for t.

`y= √(t)`

`y ^ 2 = t` because
`t> 0`

As
`t = y ^ 2` and also
`t = (x + 1)/(2)`

Then:

`y ^ 2 = (x + 1)/(2)`