Answer
Option B
Work Step by Step
Given $4x^2+y^2+32x-10y+85=0$
We can see that $a=4\\b=0\\c=1$
We will find the discriminant of the given equation $=b^2-4ac\\=0^2-4(4)(1)\\=-16$
Since $-16\lt0$ and $a\ne c$, the conic section is an Ellipse.