- #1
themadhatter1
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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]