Question

Need help with this math homework has a couple steps just need someone to guide me through itConstruct the line that is perpendicular to the directrix and passes through the focus this line will be the axis of symmetry of the para bola what are the coordinates of the point of intersection A of the access of symmetry and the directrix of the para bola explain how you can locate the vertex V of the para bola with the given focus and directrix write the coordinates of the vertex When done which way were the para bola open and can you find the value of P is it positive or negative write the equation of the parabola in vertex form

Answer 1

Part A)

The equation of the directrix is x=-5+8=3, x=3

Part B)

After using 'Perpendicular line' tool and 'Intersect' tool, we obtain the purple line and point A. A=(3,2)

The vertex V has to be on the axis of symmetry, halfway between points A and F. Vertex is V=(-1,2)

Part 3)

The focus is to the left of the vertex; therefore, the parabola opens to the left.

In general,

`\begin{gathered} Vertex:\left(h,k\right) \\ Focus:\left(h+p,k\right) \end{gathered}`

Then, in our case,

`\begin{gathered} \Rightarrow\left(h,k\right)=\left(-1,2\right) \\ and \\ \left(h+p,k\right)=\left(-5,2\right) \end{gathered}`

Thus, p=-4

Finding the equation in vertex form,

`\begin{gathered} x=(1)/(4*-4)\left(y-2\right)^2-1 \\ \Rightarrow x=-(1)/(16)\left(y-2\right)^2-1 \end{gathered}`

The answer is x=-(y-2)^2/16-1