Precalculus Homework question

Question

write an equation for the porabola that satisfies the conditions  a focus at (-2,0), directrix at x= -4

Answer 1

With what's given, you have a parabola that opens to the right. The vertex falls halfway between the focus and directrix, so it's (-3,0).

 

P is the distance between the vertex and each, so p = 1.

 

(x - (-3))² = 4(1)(y - 0)

(x + 3)² = 4y

 

Answer 2

The co-ordinates of the focus: (h+p,k) = (-2,0)

The equation of the directrix: x = h-p = -4

 

k=0

h+p=-2

h-p=-4

 

2h=-6 => h = -3

and p = 1

 

The equation of the parabola: (y-k)² = 4p(x-h)

For this problem then: y²= 4(x+3)