10.2. Polar Equations of Conics http://www.ck12.org
r= 2 −^3 cosθ
r( 2 −cosθ) = 3
2 r−r·cosθ= 3
2 r= 3 +r·cosθ= 3 +y
4 r^2 = 9 + 6 y+y^2
4 (x^2 +y^2 ) = 9 + 6 y+y^2
4 x^2 + 4 y^2 = 9 + 6 y+y^2
4 x^2 + 3 y^3 + 6 y= 9
4 x^2 + 3 (y^2 + 2 y+ 1 ) = 9 + 3
4 x^2 + 3 (y+ 1 )^2 = 12
x^2
3 +(y+ 1 )^2
4 =^1- Convert to the standard conic form.
r= 2 −cos(^3 θ− 30 ◦)r= 2 −cos(^3 θ− 30 ◦)·(^12)
12 =
(^32)
1 −^12 ·cos(θ− 30 ◦)=
3 ·^12
1 −^12 ·cos(θ− 30 ◦)
k= 3 , e=^12 , β= 30 ◦- Expand the original equation and then translate to polar coordinates: