How do you convert 4=(x-3)^2+(y-5)^24=(x−3)2+(y−5)2 into polar form?

1 Answer
George C.
May 2, 2016

r^2 - 2r(3 cos theta + 5 sin theta) + 30 = 0r2−2r(3cosθ+5sinθ)+30=0

Explanation:

To convert into polar form, substitute:

{ (x = r cos theta), (y = r sin theta) :}

4 = (r cos theta - 3)^2+(r sin theta - 5)^2

=r^2 cos^2 theta - 6r cos theta + 9 + r^2 sin^2 theta - 10r sin theta + 25

=r^2 (cos^2 theta + sin^2 theta) - 2r(3cos theta + 5 sin theta)+34

=r^2 - 2r(3 cos theta + 5 sin theta) + 34

Subtract 4 from both ends to get:

r^2 - 2r(3 cos theta + 5 sin theta) + 30 = 0

Related questions
See all questions in Converting Between Systems
Impact of this question
1505 views around the world
You can reuse this answer
Creative Commons License