Find the rectangular equation for the given polar coordinates:

Question

R=(7/(5+4sin theta))

Answer 1

r = 7/(5+4sinθ)
r(5+4sinθ) = 7
5r + 4rsinθ = 7
5r = 7 - 4y
25r^2 = (7-4y)^2
25x^2 + 25y^2 = 49 - 56y + 16y^2
25x^2 + 9y^2 + 56y = 49
25x^2 + 9(y+28/9)^2 = 49 + 9(28/9)^2
25x^2 + 9(y+28/9)^2 = 1225/9
x^2/9 + (y+28/9)^2/25 = (7/9)^2

See

http://www.wolframalpha.com/input/?i=r+%3D+7%2F%285%2B4sin%CE%B8%29