# How do you convert r= 9 into cartesian form?

How do you convert r= 9 into cartesian form?

ReportAnswer 1

Use the equality ${r}^{2} = {x}^{2} + {y}^{2}$ to find the converted form
${x}^{2} + {y}^{2} = 81$

#### Explanation:

The question How do you convert rectangular coordinates to polar coordinates? has a list of equations used when converting between polar and rectangular systems along with their derivations.

For this problem, we will be using
${r}^{2} = {x}^{2} + {y}^{2}$

If we square both sides of the of $r = 9$ we get

${r}^{2} = 81$

Now we can use the above equality to substitute in $x$ and $y$ to get

${x}^{2} + {y}^{2} = 81$

Note that this should make sense intuitively, as $r = 9$ in polar coordinates is all points of distance $9$ from the origin, that is, a circle of radius $9$ centered at the origin, and the formula for a circle of radius $s$ centered at $\left(h , k\right)$ in Cartesian coordinates is ${\left(x - h\right)}^{2} + {\left(y - k\right)}^{2} = {s}^{2}$.
Thus a circle of radius $9$ centered at the origin would have the formula ${\left(x - 0\right)}^{2} + {\left(y - 0\right)}^{2} = {9}^{2}$

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