Mathematics, 03.02.2020 20:49 lillymt1023
Convert: 6y + y² = x² from rectangular to polar form.
Answers: 3
![\bf 6y+y^2=x^2\implies \cfrac{6y}{x^2}+\cfrac{y^2}{x^2}=1\implies \cfrac{6rsin(\theta )}{[rcos(\theta )]^2}+\cfrac{[rsin(\theta )]^2}{[rcos(\theta )]^2}=1 \\\\\\ \cfrac{6rsin(\theta )}{r^2cos^2(\theta )}+\cfrac{r^2sin^2(\theta )}{r^2cos^2(\theta )}=1\implies \cfrac{6sin(\theta )}{rcos^2(\theta )}+\cfrac{sin^2(\theta )}{cos^2(\theta )}=1](/tpl/images/0497/7775/88a0d.png)
![\bf \cfrac{6sin(\theta )}{rcos^2(\theta )}=1-\cfrac{sin^2(\theta )}{cos^2(\theta )}\implies \cfrac{6sin(\theta )}{1-\frac{sin^2(\theta )}{cos^2(\theta )}}=rcos^2(\theta ) \\\\\\ \cfrac{6sin(\theta )}{cos^2(\theta )\left[ 1-\frac{sin^2(\theta )}{cos^2(\theta )} \right]}=r\implies \cfrac{6sin(\theta )}{cos^2(\theta )-sin^2(\theta )}=r \\\\\\ \cfrac{6sin(\theta )}{cos(2\theta )}=r](/tpl/images/0497/7775/ab6fe.png)
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Convert: 6y + y² = x² from rectangular to polar form....
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