Equation of a parabola given the vertex and focus is:

(

*x*–

*h*)^2 = 4

*p*(

*y*–

*k*)

The vertex (h, k) is 4, -2

The distance is p, and since the y coordinates of -2 are equal, the distance is 6 - 4 = 2.

So p = 2

Our parabola equation becomes:

(x - 4)^2 = 4(2)(y - -2)

**(x - 4)^2 = 8(y + 2)**

Latus rectum of a parabola is 4p, where p is the distance between the vertex and the focus

LR = 4p

LR = 4(2)

**LR = 8**