What are the Polar Equations of the Polar Curves that are being defined by the following statements

Circle - oriented along negative x-axis - radius a/2

r=a cosθ, a<0

Circle - oriented along positive x-axis - radius a/2

r=a cosθ, a>0

Circle - oriented along negative y-axis - radius a/2

r=a sinθ, a<0

Circle - oriented along the positive y-axis - radius a/2

r=a sinθ, a>0

Limaçon -with a loop -oriented along the positive x-axis

r=a+b cos⁡θ, where 0<a/b<1

Limaçon -with a dent -oriented along the positive x-axis

r=a+b cos⁡θ, where 1<a/b<2

Limaçon -cardioid -oriented along the positive x-axis

r=a+b cos⁡θ, where a/b=1

Limaçon -convex -oriented along the positive x-axis

r=a+b cos⁡θ, where a/b≥2

Limaçon -with a loop -oriented along the positive y-axis

r=a+b sin⁡θ, where 0<a/b<1

Limaçon -with a dent -oriented along the positive y-axis

r=a+b sin⁡θ, where 1<a/b<2

Limaçon -cardioid -oriented along the positive y-axis

r=a+b sin⁡θ, where a/b=1

Limaçon -convex -oriented along the positive y-axis

r=a+b sin⁡θ, where a/b≥2

Limaçon -with a loop -oriented along the negative x-axis

r=a-b cos⁡θ, where 0<a/b<1

Limaçon -with a dent -oriented along the negative x-axis

r=a-b cos⁡θ, where 1<a/b<2

Limaçon -cardioid -oriented along the negative x-axis

r=a-b cos⁡θ, where a/b=1

Limaçon -convex -oriented along the negative x-axis

r=a-b cos⁡θ, where a/b≥2

Limaçon -with a loop -oriented along the negative y-axis

r=a-b sin⁡θ, where 0<a/b<1

Limaçon -with a dent -oriented along the negative y-axis

r=a-b sin⁡θ, where 1<a/b<2

Limaçon -cardioid -oriented along the negative y-axis

r=a-b sin⁡θ, where a/b=1

Limaçon -convex -oriented along the negative y-axis

r=a-b sin⁡θ, where a/b≥2

rose with 2n petals

r=acos(nθ), r=asin(nθ), where n is even

rose with n petals

r=acos(nθ), r=asin(nθ), where n is odd

Circle with a radius k

r=k

Line -with a slope of -a/b -with y-intercept k/b

r=k/(a cos⁡θ+b sin⁡θ )

Spiral with respect to θ

r=θ

Lemniscate symmetric to the polar axis, to θ = π/2 , and the pole

r²=a²cos2θ

Lemniscate symmetric to the pole

r²=a²sin2θ

A line that coincides with the terminal side of the angle θ=k

θ=k