The focus, directrix and axis of symmetry of the parabola [tex]y^{2} = 16\cdot x[/tex] are [tex](x,y) = (0, 4)[/tex], [tex]x = -4[/tex] and [tex]y = 0[/tex].
The equation of the parabola in standard form is defined below:
[tex]4\cdot a\cdot (x- h) = (y-k)^{2}[/tex] (1)
Where:
- [tex](h,k)[/tex] - Vertex.
- [tex]a[/tex] - Distance between focus and vertex.
- [tex](x, y)[/tex] - Independent and dependent variables.
The coordinates of the focus are [tex](x,y) = (0, h+a)[/tex] and the equation of the directrix is [tex]x = h-a[/tex]. Lastly, the equation of the axis of symmetry is [tex]y = k[/tex].
If we know that [tex]h = 0[/tex], [tex]k = 0[/tex] and [tex]a = 4[/tex], then the focus, directrix and axis of symmetry of the parabola are:
Focus
[tex](x,y) = (0, 4)[/tex]
Directrix
[tex]x = -4[/tex]
Axis of symmetry
[tex]y = 0[/tex]
The focus, directrix and axis of symmetry of the parabola [tex]y^{2} = 16\cdot x[/tex] are [tex](x,y) = (0, 4)[/tex], [tex]x = -4[/tex] and [tex]y = 0[/tex].
We kindly invite to check this question on parabolae: https://brainly.com/question/4074088
