http://www.ck12.org Chapter 10. Polar and Parametric Equations
(x− 3 )^2 +(y+ 4 )^2 = 25
x^2 − 6 x+ 9 +y^2 + 8 y+ 16 = 25
r^2 − 6 x+ 8 y= 0
r^2 − 6 r·cosθ+ 8 r·sinθ= 0
r−6 cosθ+8 sinθ= 0
r=6 cosθ−8 sinθPractice
Convert the following conics from polar form to rectangular form. Then, identify the conic.
1.r= 3 −cos^5 θ
2.r= 2 −cos^4 θ
3.r= 2 −cos^2 θ
4.r= 2 −4 cos^3 θ
5.r=5 cos(θ)
Graph the following conics.
6.r= 4 −2 cos^5 (θ− 90 ◦)
7.r= 3 −7 cos^5 (θ− 60 ◦)
8.r= 3 −3 cos^3 (θ− 30 ◦)
9.r= 2 −cos(^1 θ− 60 ◦)
10.r= 6 −3 cos^3 (θ− 45 ◦)
Translate the following conics to polar form.
11.(x− 41 )^2 +y 32 = 1
12.(x− 5 )^2 +(y+ 12 )^2 = 169
13.x^2 +(y+ 1 )^2 = 1
14.(x− 1 )^2 +y^2 = 1
15.− 3 x^2 − 4 x+y^2 − 1 = 0