Converting rectangular equation to polar form

X^2=y (8-y)

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.