- Let $x=2u+3$ and $y=4v-5$. Complete the $u,v,x,y$ table below, and then construct a graph of both $u^2+v^2=1$ and the corresponding equation in the $xy$ plane. $$ \begin{array}{c|c|c|c} u&v&x&y\\\hline 0&0&3&-5\\ 1&0&5&-5\\ 0&1&&\\ -1&0&&\\ 0&-1&&\\ \end{array} $$
- Draw $\ds \frac{(x-2)^2}{16}+\frac{(y-3)^2}{9}=1$.
- Draw $x^2+4x+y^2-10y=7$ by first completing the square.
- Draw $\ds \frac{(x-2)^2}{16}-\frac{(y-3)^2}{9}=1$.
- Draw $\ds \frac{(y-3)^2}{9}-\frac{(x-2)^2}{16}=1$.
- Draw $x^2-6x+2y^2+8y=8$ by first completing the square.
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