Respuesta :
An equation for the parabola would be y²=-19x.
Since we have x=4.75 for the directrix, this tells us that the parabola's axis of symmetry runs parallel to the x-axis. This means we will use the standard form
(y-k)²=4p(x-h), where (h, k) is the vertex, (h+p, k) is the focus and x=h-p is the directrix.
Beginning with the directrix:
x=h-p=4.75
h-p=4.75
Since the vertex is at (0, 0), this means h=0 and k=0:
0-p=4.75
-p=4.75
p=-4.75
Substituting this into the standard form as well as our values for h and k we have:
(y-0)²=4(-4.75)(x-0)
y²=-19x
Since we have x=4.75 for the directrix, this tells us that the parabola's axis of symmetry runs parallel to the x-axis. This means we will use the standard form
(y-k)²=4p(x-h), where (h, k) is the vertex, (h+p, k) is the focus and x=h-p is the directrix.
Beginning with the directrix:
x=h-p=4.75
h-p=4.75
Since the vertex is at (0, 0), this means h=0 and k=0:
0-p=4.75
-p=4.75
p=-4.75
Substituting this into the standard form as well as our values for h and k we have:
(y-0)²=4(-4.75)(x-0)
y²=-19x
From the information given, the equation of the parabola is:
[tex]x = -19y^2[/tex]
The equation of a parabola with vertex (h,k) is given, and directrix at the x-axis, by:
[tex]x = a(y - k)^2 + h[/tex]
In this problem:
- Vertex at the origin, hence [tex]k = h = 0[/tex].
- Directrix at x = 4.75, hence [tex]-\frac{a}{4} = 4.75 \rightarrow a = -19[/tex]
Then, the equation of the parabola is:
[tex]x = a(y - k)^2 + h[/tex]
[tex]x = -19(y - 0)^2 + 0[/tex]
[tex]x = -19y^2[/tex]
A similar problem is given at https://brainly.com/question/17987697
