find the equation of a parabola

Question

Find the equation of a parabola through (-15/4 , 2) and (0,-1) whose axis is parallel to the x axis and latus rectum is 4.

 

 

Please help

Answer 1

parabola through (-15/4, 2) and (0,-1)

latus rectum = 4 = distance from one side of the parabola to the other, across the focus

focus and directrix are equidistant from the vertex

all points (x,y) on the parabola are equidistant from the focus and directrix

the directix is a line x= a constant

axis is parallel to the x axis

it's a horizontal parabola since its axis is parallel to y=0

the parabola's axis is the axis of symmetry,

general form of the equation is

x= a(y-k)^2 +h where (h,k) is the vertex

0= a(-1-k)^2 +h

and

-15/4 = a(2-k)^2 +h

and