Answer
See below
Work Step by Step
Given $21y^2-210y-4x^2=-441$
We can see that $a=-4\\b=0\\c=21$
We will find the discriminant of the given equation $=b^2-4ac\\=0^2-4(-4)(21)\\=336$
The conic is an hyperbola.
To graph the hyperbola, first complete the square in x.
$21y^2-210y-4x^2=-441\\21(y^2-10y+25-25)-4x^2=-441\\21(y-5)^2-25(21)-4x^2=-441\\21(y-5)^2-4x^2=84\\\frac{(y-5)^2}{4}-\frac{x^2}{21}=1$
From the equation, you can see that the center is at $(5,0)$ and the vertices are at $(7,0)$ and $(3,0)$.
