Posted by **A** on Friday, August 12, 2011 at 7:21am.

r=8cos(theta)+5sin(theta), convert the polar equation into a rectangular equation and then complete the square and determine the center radius...?

Help?! I missed the section, and am not getting anywhere with the text...

- Trig/pre-calc -
**Reiny**, Friday, August 12, 2011 at 7:48am
In your text, you should find a diagram similar to this one

http://en.wikipedia.org/wiki/File:Polar_to_cartesian.svg

If you label the endpoint of the rotating arm as either

(x,y) in rectangular and (r,Ų) in polar, then

x = rcosŲ or cosŲ = x/r

y = rsinŲ or sinŲ = y/r

also x^2 + y^2 = r^2, and tanŲ = y/x

then in your equation r = 8(x/r) + 5(y/r)

multiply by r

r^2 = 8x + 5y

x^2 + y^2 = 8x + 5y

x^2 - 8x + y^2 - 5y = 0

This is the equation of a circle. I will assume you know how to complete the square and thus find the centre and radius.

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