# Convert the following polar equations to rectangular equations. a. r=1/(4sinx-3sinx) b.r=4

Convert the following polar equations to rectangular equations.
a. $r=\frac{1}{4\mathrm{sin}x-3\mathrm{sin}x}$
b.r=4
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Step 1
To Determine:
Convert the following polar equations to rectangular equations.
a.$\frac{1}{4\mathrm{sin}x-3\mathrm{sin}x}$
b. r =4
Step 2
Explanation:
a.
Given that,
$r=\frac{1}{4\mathrm{sin}x-3\mathrm{sin}x}=\frac{1}{\mathrm{sin}x}$
Multiply both the side r
${r}^{2}=\frac{r}{\mathrm{sin}x}$
We know that,
${r}^{2}={x}^{2}+{y}^{2}$
${x}^{2}+{y}^{2}=\frac{r}{\mathrm{sin}x}$
and we know that,
$y=r\mathrm{sin}x$
$r=\frac{y}{\mathrm{sin}x}$
Put the value of r
${x}^{2}+{y}^{2}=\frac{y}{\mathrm{sin}x}/\left(\mathrm{sin}x\right)$
${x}^{2}+{y}^{2}=\frac{y}{{\mathrm{sin}}^{2}x}$