Given equation :
y2 = -6x
Comparing given equation with parabola having equation,
y2 = - 4ax
4a = 6
a = \(\frac{3}{2}\)
Focus : F(-a,0) = F\(\Big(-\frac{3}{2},0\Big)\)
Vertex : A(0,0) = A(0,0)
Equation of the directrix : x - a = 0
x - \(\frac{3}{2}\) = 0
x = \(\frac{3}{2}\)
Lenth of latusrectum : 4a = 6