70

find the focus, directrix, and equation of the parabola in the graph.

Option B

Part a) The focus is

Part b) The directrix is

Part c) The equation is  

Step-by-step explanation:

step 1

Find the equation of the parabola

we know that

The parabola in the graph has a horizontal axis.

The standard form of the equation of the horizontal parabola is

where

p≠ 0

The vertex of this parabola is at (h, k).

The focus is at (h + p, k).

The directrix is the line x= h- p.

The axis is the line y = k.

If p > 0, the parabola opens to the right, and if p < 0, the parabola opens to the left

In this problem we have that the vertex is the origin

so

(h,k)=(0,0)

substitute in the equation

The points (7,1) and (7,-1) lies on the parabola-----> see the graph

substitute the value of x and the value of y in the equation and solve for p

The equation of the horizontal parabola is

step 2

Find the focus

we know that

The focus is at (h + p, k)

Remember that

substitute

therefore

The focus is at

step 3

Find the directrix

The directrix is the line x = h- p

Remember that

substitute