A Date in the Polar Coordinate System (Part 1)

On a date, Delaney and Rebecca are plugging functions into WolframAlpha to create fun shapes (and chaotic ones, like this ). One of the shapes they make to show their love for each other is a polar curve of the form $r=k+k\sin\theta$ for some $k\in\mathbb{R}^-.$

Since Delaney forgot what class of curves that figure belonged to, Rebecca told her it was a special type of what polar figure?

Image Credit: Wikimedia Benjah-Courtney Carmody