Hola

Debemos llevar a

(x - Xv)^2 = 4 p (y - Yv)

Vértice en (Xv , Yv)

p : Distancia de vértice a foco y a directriz

Lado recto : doble de abscisa focal = abs(4 p)

4 x^2 + 48 y + 12 x = 159

x^2 + 3 x = -12 y + (159/4)

x^2 + 2*(3/2) x = -12 y + (159/4)

x^2 + 2*(3/2) x + (9/4) = -12 y + (159/4) + (9/4)

(x + (3/2))^2 = -12 y + (168/4) = -12 y + 42

(x + (3/2))^2 = -12 (y - (42/12))

(x + (3/2))^2 = 4*(-3) (y - (7/2))

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Vértice (-3/2 ; 7/2)

p = -3

Foco ( (-3/2) ; (7/2) + (-3) ) = (-9/2 ; 1/2)

Directriz

y = (-3/2) - (-3) = (-3/2) + (6/2)

y = 3/2

Lado recto

LR = abs(4 p) = 12