Question

Converting rectangular equation to polar form
X^2=y(8-y)

Answer 1

Answer: Our equation in polar form is r = 8*sin(θ)

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.