Answer: Our equation in polar form is r = 8*sin(θ)
Step-by-step explanation:
In polar form, we have that:
x = r*cos(θ)
y = r*sin(θ)
then, our equation is:
x^2 = y(8 - y) = 8y - y^2
now, we replace the variables by the expressions above:
(r*cos(θ))^2 = 8r*sin(θ) - (r*sin(θ))^2
r^2*(cos(θ)^2 + sin(θ)^2) = 8*r*sin(θ)
and (cos(θ)^2 + sin(θ)^2) = 1
so our equation is:
r^2 = 8*r*sin(θ)
we divide in both sides by r and get:
r = 8*sin(θ)
So that is our equation in polar form.
