Find the equation of the parabola with directrix x + 1 = 0 and y = 1, and the length of the latus rectum is 4. Sketch the graph.

1 answer

x+1 = 0
X = -1 = h = axis.

F(-1,Y2)
V(-1,k)
D(-1,1)

1/a = 4 = Latus rectum
a = 1/4

1/4a = 1/1 = 1

k = y+1/4a = 1 + 1 = 2.

Y2 = k+1/4a = 2 + 1 = 3.

Y = a(x-h)^2 + k
Y = 1/4(x+1)^2 + 2

Use the following points for graphing:
(x,y)
(-3,3)
(-2,9/4)
V(-1,2)
(0,9/4)
(1,3)