# pre calculus

posted by Meredith

in the equation (x-4)^2+y^2=16 the letters x and y represent rectangular coordinates. Write the equivalent equation using polar coordinates. solve for r

1. Reiny

sinØ = y/r --> y = rsinØ
cosØ = x/r --> x = rcosØ

(x-4)^2+y^2=16
(rcosØ -4)^2 + r^2sinØ = 16
r^2 cos^2 - 8rcosØ + 16 + r^2sin^2 Ø = 16
r^2 (cos^2 Ø + sin^2 Ø) - rcosØ + 16 = 16
r^2 -rcosØ = 0
r - cosØ = 0

check:
http://www.wolframalpha.com/input/?i=polar+plot+r+%3D+cos%C3%98

http://www.wolframalpha.com/input/?i=plot+(x-4)%5E2%2By%5E2%3D16

2. Steve

Clearly the graph is a circle of radius 4 with center at (4,0).

You know that r = cosθ is a circle with radius 1/2 and center at (0,1/2).

so, we have r = 8cosθ

3. Reiny

Steve has the correct equation.
I don't know why my 8 was dropped in my 3rd last line, just careless.

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