Question

Find the coordinates of the focuss and the equation of the directrix for y²=28x?

Answer 1

Focus: `(7,0)`
Directrix: `x=-7`

Explanation:

We can rewrite this equation as `x=1/28y^2`. This gives us the equation of a parabola facing the right. The origin is the vertex as there are no translations shown in the graph. To find the focus and the directrix, we should know the value of `p`. This is the distance of the vertex to both the focus and directrix. The scale factor is known as `1/(4p)` for a positive parabola. Let's apply this to our equation:

`1/(4p)=1/28`
`4p=28`
`p=7`

In a horizontal parabola, the focus will have the same y-coordinate as the vertex. Since the parabola faces the right, the focus is moved 7 units to the right:

Focus: `(0+7,0)` = `(7,0)`

The directrix is 7 units to the left of the vertex. Since we have a vertical parabola, the directrix is a vertical line, `x=-7`.