How 16x^2 +y^2 +8xy- 74x -78y +212= 0 is also an equation of parabola?

Dear student,
following is the answer to your question:

comparing the given equation with the equation $a{x}^2+2hxy+b{y}^2+2gx+2fy+c=0$
we get, a = 16, b = 1, h=4, g=-37, f=-39 and c=212  
for a general equation of second degree to represent a parabola, $∆= abc+2fgh-a{f}^2-b{g}^2- c{h}^2\ne 0$   .....(1)
and h² = ab.   ....(2)

on putting the values in equations (1) and (2), the condition for parabola are satisfied. 
Hence the given equation represents a parabola.