Question

What is the polar form of the equation? What type of polar curve is this?

Answer 1

The curve is given to be:

`x^2+y^2+12y=0`

We can rewrite the equation in the form:

`(\left(x-h\right)^2)/(a^2)+(\left(y-k\right)^2)/(b^2)=1`

Using the Completing the Square method, we have the equation to be:

`(\left(x-0\right)^2)/(6^2)+(\left(y-\left(-6\right)\right)^2)/(6^2)=1`

Therefore, the ellipse's center is (0, -6).