- #1

themadhatter1

- 140

- 0

## Homework Statement

Convert the polar equation

r = 2(h cos θ + k sin θ)

to rectangular form and verify that it is the equation of a circle. Find the radius and the rectangular coordinates of the center of the circle.

## Homework Equations

## The Attempt at a Solution

First, I multiply both sides by r and distribute.

[tex]r^2=2hr\cos\theta+2kr\sin\theta[/tex]

apply the x= r cos θ and y= r sin θ equations

[tex]r^2=2hx+2ky[/tex]

from here I can factor out the 2 and plug it into the equation for a circle.

[tex]x^2+y^2=2(hx+ky)[/tex]

not quite sure what do do from here.

The answer to the problem is supposed to be:

[tex](x-h)^2+(y-k)^2=h^2+k^2; \sqrt{h^2+k^2}; (h,k)[/tex]