Identify a conic section without completing the square

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A nondegenerate conic section of the form

Ax^2+Cy^2+Dx+Ey+F=0

… in which A and C are not both zero, is

○ A circle if A = C,
○ A parabola if AC = 0,
○ An ellipse if A ≠ C and AC greater than 0, and
○ A hyperbola if AC less than 0

Q. Identify the graph of each of the following nondegenerate conic sections:

a) x^2+y^2−6x+y+3=0

b) y^2−12x−4y+52=0

c) 4x^2−24x−9y^2−90y−153=0