Describe the graph of the parametric equations $x=e^{6 t}, y=e^{12 t},-\infty

Question

Describe the graph of the parametric equations $x=e^{6 t}, y=e^{12 t},-\infty<t<\infty$.
A) The parabola $y=x^{2}$.
B) The right half of the parabola $y=x^{2}$.
C) The circle $x^{2}+y^{2}=36$.
D) The top half of the circle $x^{2}+y^{2}=36$.

Quizplus · Accepted Answer

The parametric equations can be rewritten as $y = (e^{6t})^2 = x^2$, which describes the parabola $y = x^2$. Since $x = e^{6t}$ is always positive, the graph represents the right half of the parabola.

Describe the Graph of the Parametric Equations x=e6t,y=e12t,−∞<t<∞x=e^{6 t}, y=e^{12 t},-\infty<t<\inftyx=e6t,y=e12t,−∞<t<∞

Describe the Graph of the Parametric Equations $x=e^{6 t}, y=e^{12 t},-\infty<t<\infty$