Given equation :
3x2 = -16y
x2 = \(-\frac{16}{3}y\)
Comparing the given equation with parabola having an equation,
x2 = 4ay
4a = \(\frac{16}{3}\)
a = \(\frac{4}{3}\)
Focus : F(0,-a) = F\(\Big(0,-\frac{4}{3}\Big)\)
Vertex : A(0,0) = A(0,0)
Equation of the directrix : y - a = 0
y - \(\frac{4}{3}\) = 0
y = \(\frac{4}{3}\)
Lenth of latusrectum :
4a = \(\frac{16}{3}\)