Question Convert parametric equations $x=-\frac{t^{2}}{3}, y=t$ to rectangular form.

Studdy Solution

STEP 1

Assumptions
1. The given parametric equations are: \begin{aligned} x &= -\frac{t^{2}}{3}, \\ y &= t. \end{aligned} \]
2. We need to eliminate the parameter t $to rewrite the equations in rectangular form (also known as Cartesian form), which involves only$ x $and$ y$.

STEP 2

We will solve the second equation for $t$ to express $t$ in terms of $y$ .
$t = y$

STEP 3

Now, we will substitute the expression for $t$ from STEP_2 into the first equation to eliminate the parameter $t$ .
$x = -\frac{t^{2}}{3}$

STEP 4

Replace $t$ with $y$ in the equation from STEP_3.
$x = -\frac{y^{2}}{3}$

STEP 5

The equation from STEP_4 is now in rectangular form, as it only contains $x$ and $y$ .
The rectangular form of the given parametric equations is:
$x = -\frac{y^{2}}{3}$
This is the final solution.

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