Let me add some more details abut the parabola before applying a formula,

1. Recognize the type, vertical(regular) or horizontal(sideways).

The difference in the two types is in which variable is squared:

for vertical parabolas, the x part is squared and for horizontal, the y part is squared.

Here, for the question, the directrix is x=-5, it means that the graph type is horizontal.

2. Remember or you can derive the formula from y= ax^{2} + bx +c for the vertical, or x= ay^{2} + by + c for the horizontal,

such that, the vertex form of a parabola equation with its vertex at (h, k) as,

y = a(x – h)^{2} + k → 1/a( y - k) = (x - h)^{2}, for the vertical

x = a(y – k)^{2} + h, → 1/a(x - h )= (y - k)^{2}, for the horizontal

Or, the conics form of the parabola equation as

4p(y – k) = (x – h)^{2}, for the vertical

4p(x – h) = (y – k)^{2}, for the horizontal

where 4p = 1/a, or a= 1/(4p).

*Keep h with x, y with k, and p with the first degree part (not squared part)*

The* conic form* is more useful because the variable p represents the distance between the vertex and the focus. Also, the same p represents the distance from the vertex to the directrix. The vertex is exactly midway between the directrix and the focus. Obviously, 2p represents the distance between the focus and the directrix.

3. Find the variables for the formula recognized.

For the given question, the formula to be

4p(x – h) = (y – k)^{2}, for the horizontal

From the focus (5,0) and the directrix is x=-5 given,

the value of h (which stays with x) is located in the middle of 5 and -5, that is 0,

and k (which stays with y) is the same y value of the focus, that is 0, therefore the vertex is at (0,0)

P is the distance of x-axix between the vertex and the focus, that is p = 5-0 = 5

Replace all the variables into the formula: 4(5)(x - 0) = (y - 0)^{2 }→ **20x = y****2,**^{ }or** y**^{2} = 20x

I hope that this explanation helps to understand the parabola, and to remember its formula. This is one of the formula easy to get confused and forget.

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