Step 1
A nondegenerate conic section of the form
\(Ax^2 + Cy^2 + Dx + Ey + F = 0\)
a)If \(A = C\) then circle
b)If \(AC = 0\) then the parabola
c)If \(A \neq C\) and \(AC > 0\) then the ellipse
d)If \(AC < 0\) then hyperbola.
Step 2
Given equation of conics is
\(y^2 - 12x - 4y + 52 = 0\)
comparing with \(Ax^2 + Cy^2 + Dx + Ey + F = 0\) gives
\(A=0 ,C=1 , D=-12 , E=-4 , F=0\)
Here \(AC = 0 (1) = 0\)
Therefore the graph of the given equation is parabola.