find the equation for a parabola which fits given criteria t

find the equation for a parabola which fits given criteria the endpoints of latus rectum are (-1,-7) and (5,-7)

endpoints of latus rectum = (-1,-7) and (5,-7)

calculating the distance between endpoints of latus rectum

distance = sqrt ( x2-x1)^2 + ( y2 - y1)^2

distance = 6

focus = (2,-7)

standard equation of parabola is

(x-h)^2 = 4p(y-k)

4p = 6

p = 6/4 = 3/2

vertex = ( 2 , -7-3/2 ) = 2,-17/2

hence, equation of parabola is

(x-2)^2 = 6 ( y + 17/2 )