find the graph and rectangular equation of the curve whose parametric equation is given. x = 6t², y = t + 1…

find the graph and rectangular equation of the curve whose parametric equation is given. x = 6t², y = t + 1; -∞ < t < ∞

find the graph and rectangular equation of the curve whose parametric equation is given. x = 6t², y = t + 1; -∞ < t < ∞

Answer

Answer:

The rectangular equation is $x = 6(y - 1)^2$.

Explanation:

Step1: Solve for $t$ from $y$ - equation

$y=t + 1$, so $t=y - 1$.

Step2: Substitute $t$ into $x$ - equation

Substitute $t=y - 1$ into $x = 6t^2$. We get $x=6(y - 1)^2$. This is a parabola that opens to the right. The vertex of the parabola is at the point $(0,1)$. As $y$ varies from $-\infty$ to $\infty$, $x = 6(y - 1)^2\geq0$.