- Give an equation of a plane that passes through the point $(2,3,5)$ and has normal vector $(-2,1,3)$.
- Give an equation of a plane that passes through the 3 points $(2,0,0)$, $(0,3,0)$, $(0,0,5)$.
- Give a vector equation of the line of intersection of the two planes $x+y+z=2$ and $3x-2z=1$.
- Draw the three circles $x^2+y^2=1$, $(x-2)^2+(y-5)^2=1$, and $(x+2)^2+(y+3)^2=1$.
- Draw $\left(\frac{x}{3}\right)^2+\left(\frac{y}{5}\right)^2=1$.
- Let $x=2u+3$ and $y=4u-5$. Complete the $u,v,x,y$ table below, and then construct a graph of both $v=u^2$ and the corresponding equation in the $xy$ plane.
$$ \begin{array}{c|c|c|c} u&v&x&y\\\hline 0&0&3&-5\\ 1&0&5&-5\\ 0&1&&\\ 1&1&&\\ -1&1&&\\ 2&4&&\\ -2&4&&\\ \end{array} $$
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