Find parametric equations for the given curve. (x+9)2+(y−4)2=49

Question

Find parametric equations for the given curve.  (x+9)2+(y−4)2=49

Stephanie Mann · Accepted Answer

Step 1
To find the parametric equation of the given curve
${(x + 9)}^{2} + {(y - 4)}^{2} = 49$
Given equation is in the form of equation of a circle given by
${(x - h)}^{2} + {(y - k)}^{2} = r^{2}$ with center (h,k) and radius r.
The parametric equations of a circle is given by
$s (t) = {\begin{cases} x (t) = r \cos (t) + h \\ y (t) = r \sin (t) + k \end{cases}$
From the given equation ${(x + 9)}^{2} + {(y - 4)}^{2} = 49$ , we have
$h = - 9, k = 4$ and $r^{2} = 49 \Rightarrow r = 7$
Step 2
Then the parametric equations of the given circle is
$s (t) = {\begin{cases} x (t) = r \cos (t) + h \\ y (t) = r \sin (t) + k \end{cases}, [0, 2 π]$
$s (t) = {\begin{cases} x (t) = 7 \cos (t) - 9 \\ y (t) = 7 \sin (t) + 4 \end{cases}, [0, 2 π]$

Find parametric equations for the given curve. (x+9)^{2}+(y-4)^{2}=49

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