# Eliminate the parameter and obtain the standard form of the rectangular equation.Circle: x = h + r cos(?), y = k + r sin(?)Use your result to find a set of parametric equations for the line or conic section. (When 0 leq ? leq 2?.)Circle: center: (6, 3), radius: 7

Eliminate the parameter and obtain the standard form of the rectangular equation. Circle: $x=h+r\mathrm{cos}\left(?\right),y=k+r\mathrm{sin}\left(?\right)$ Use your result to find a set of parametric equations for the line or conic section. Circle: center: (6, 3), radius: 7

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stuth1

Step 1: Given $x=h+r\mathrm{cos}\theta ,y=k+\mathrm{sin}\theta$

Step 2: Solution $x=h+r\mathrm{cos}\theta ,y=k+\mathrm{sin}\theta$
$x-h=r\mathrm{cos}\theta ,y-k=r\mathrm{sin}\theta$

Squaring and adding $\left(x-h{\right)}^{2}+\left(y-k{\right)}^{2}={r}^{2}{\mathrm{sin}}^{2}\theta +{r}^{2}{\mathrm{cos}}^{2}\theta$
$\left(x-h{\right)}^{2}+\left(y-k{\right)}^{2}={r}^{2}$

With (6,3), radius = 7 $x=6+7\mathrm{cos}\theta$
$7=3+7\mathrm{sin}\theta$