consider the polar equation

r=7 cos(θ+ pi divided by 4)

A) change the equation to rectangular coordinates.

B) by completing the square, obtain the Standard form of this well-known equation.

I NEED HELP WITH THIS PROBLEM I DON'T KNOW WHERE TO START.

1 answer

r = 7cos(θ+π/4)
r^2 = 7rcos(θ+π/4)
x^2+y^2 = 7/√2 r(cosθ-sinθ)
x^2+y^2 = 7/√2 (x-y)

You can massage that into the standard circle form if you want. Or, cheat here:

http://www.wolframalpha.com/input/?i=x^2%2By^2+%3D+7%2F%E2%88%9A2+%28x-y%29