# How do you convert 3=(7x-5y)^2-y into polar form?

##### 1 Answer
Apr 23, 2018

Put $x = r \cos \theta$ and $y = r \sin \theta$

#### Explanation:

$3 = {\left(7 x - 5 y\right)}^{2} - y$ ...............(Given equation)

Put $x = r \cos \theta$ and $y = r \sin \theta$ ; we get :-

$\Rightarrow 3 = {\left(7 r \cos \theta - 5 r \sin \theta\right)}^{2} - r \sin \theta$

$\Rightarrow 3 = 49 {r}^{2} {\cos}^{2} \theta + 25 {r}^{2} {\sin}^{2} \theta - 70 {r}^{2} \cos \theta . \sin \theta - r \sin \theta$

$\Rightarrow 3 = 24 {r}^{2} {\cos}^{2} \theta + \left(25 {r}^{2} {\cos}^{2} \theta + 25 {r}^{2} {\sin}^{2} \theta\right) - 70 {r}^{2} \cos \theta . \sin \theta - r \sin \theta$

$\Rightarrow 3 = 24 {r}^{2} {\cos}^{2} \theta + 25 {r}^{2} - 70 {r}^{2} \cos \theta . \sin \theta - r \sin \theta$

$\therefore 25 {r}^{2} + 24 {r}^{2} {\cos}^{2} \theta - 70 {r}^{2} \cos \theta . \sin \theta - r \sin \theta - 3 = 0$

is the Polar form