CPM Homework Help : PC3 Problem 11-66

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11-66.

Rewrite each of the following equations in polar form.

$6x − x^2 = y^2$
Hint (a):
$r^2=x^2+y^2$
Step 1(a):
$6r\cos(\theta)-r^2\cos^2(\theta)=r^2\sin^2(\theta)$
Step 2(a):
$6r\cos(\theta)=r^2\cos^2(\theta)+r^2\sin^2(\theta)$
Step 3(a):
$6r\cos(\theta)=r^2\left(\cos^2(\theta)+\sin^2(\theta)\right)$

$2x + 3y = 5$
Hint (b)
$x=r\cos(\theta)$
Step 1(b):
$2r\cos(\theta)+3r\sin(\theta)=5$
Step 2(b):
$r\left(2\cos(\theta)+3\sin(\theta)\right)=5$

$x^2 + y^2 = 7$
Hint (c)
$y=r\sin(\theta)$
Step (c):
$r^2=7$

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