Question

PLS HELP

Write the equation of a parabola with vertex (-5,8) and directrix x=2. Show all of your work and put your equation in graphing/vertex form.

Answer 1

`(y - 8)^(2) = - 28(x + 5)`

Step-by-step explanation

The given parabola has vertex at (-5,8).

and directrix at: x=2,

This implies that the axis of symmetry of the parabola is parallel to the x-axis.

This parabola has equation of the form:

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

where (h,k)=(-5,8) is the vertex.

`(y - 8)^(2) = 4p(x - - 5)`

and p =-5-2=-7

Hence the equation becomes,

`(y - 8)^(2) = 4( - 7)(x + 5)`

`(y - 8)^(2) = - 28(x + 5)`

Answer 2

The given parabola has vertex at (-5,8).

and directrion at: x=2,

So

axis of symmetry of the parabola is parallel to the x-axis.

This parabola has equation of the form:

(y - k)² = 4p(x - h)(y−k)

where (h,k)=(-5,8) is the vertex.

(y - 8)² = 4p(x -( - 5))(y−8)

and p =-5-2=-7

Hence the equation becomes,

(y - 8)²= 4( - 7)(x + 5)

(y-8)²+28(x+5)=0

is a required equation.