Parametric Functions, Vectors, and Matrices — Quiz 1

Questions in this quiz (7)

1. Which of the following choices is a pair of parametric equations for the ellipse $$\frac{(x+2)^2}{9}+\frac{(y-1)^2}{16}=1$$?

   • $$x(t)=-2+3\cos t,\ y(t)=1+4\sin t$$
   • $$x(t)=3\cos t,\ y(t)=4\sin t$$
   • $$x(t)=-2+4\cos t,\ y(t)=1+3\sin t$$
   • $$x(t)=2+3\cos t,\ y(t)=-1+4\sin t$$

2. Which of the following choices is a pair of parametric equations for the hyperbola $$\frac{(x-1)^2}{16}-\frac{(y+2)^2}{9}=1$$?

   • $$x(t)=1+4\cos t,\ y(t)=-2+3\sin t$$
   • $$x(t)=1+4\sec t,\ y(t)=-2+3\tan t$$
   • $$x(t)=-1+4\sec t,\ y(t)=2+3\tan t$$
   • $$x(t)=1+3\sec t,\ y(t)=-2+4\tan t$$

3. Find the rectangular equation for the curve given by the parametric equations $$x(t)=t+2,\ y(t)=t^2+4,\ -2\le t\le 2$$.

   • $$y=x^2$$
   • $$y=x^2-4x+8$$
   • $$y=x^2+4x+4$$
   • $$y=x^2-2x+4$$

4. Find the rectangular equation for the curve given by the parametric equations $$x(t)=\cos t,\ y(t)=1+\sin^2 t,\ 0\le t\le \pi$$.

   • $$y=2-x^2$$
   • $$y=1+x^2$$
   • $$y=1-x^2$$
   • $$y=x^2$$

5. Which of the following choices represents a set of parametric equations that represents the graph of $$y=\sqrt{x+1}$$ using the parameter $$t=x+1$$?

   • $$x(t)=t-1,\ y(t)=\sqrt{t},\ t\ge 0$$
   • $$x(t)=t+1,\ y(t)=\sqrt{t},\ t\ge 0$$
   • $$x(t)=t-1,\ y(t)=\sqrt{t+1},\ t\ge 0$$
   • $$x(t)=t,\ y(t)=\sqrt{t+1},\ t\ge 0$$

6. Find the rectangular form of the equation of a line represented by the parametric equations $$x(t)=2-3t,\ y(t)=1+2t$$.

   • $$y-1=-\frac{2}{3}(x-2)$$
   • $$y-1=\frac{2}{3}(x-2)$$
   • $$y+1=\frac{2}{3}(x-2)$$
   • $$y-2=\frac{3}{2}(x-1)$$

7. Which of the following represents the parametrization of the line through the points $$(1,3)$$ and $$(5,7)$$?

   • $$x(t)=1+4t,\ y(t)=3+4t$$
   • $$x(t)=1+4t,\ y(t)=3+2t$$
   • $$x(t)=1+2t,\ y(t)=3+4t$$
   • $$x(t)=5-4t,\ y(t)=7-2t$$