Respuesta :

[tex]\bf \textit{parabola vertex form with focus point distance}\\\\ \begin{array}{llll} \boxed{(y-{{ k}})^2=4{{ p}}(x-{{ h}})} \\\\ (x-{{ h}})^2=4{{ p}}(y-{{ k}}) \\ \end{array} \qquad \begin{array}{llll} vertex\ ({{ h}},{{ k}})\\\\ {{ p}}=\textit{distance from vertex to }\\ \qquad \textit{ focus or directrix}\\\\ 4p=focal\ width \end{array}\\\\ -------------------------------\\\\ x^2=12y\implies (x-0)^2=12(y-0)\quad \begin{cases} h=0\\ k=0\\ \boxed{4p=12} \end{cases}[/tex]

Length of focal width is 12.

What is focal width?

Focal Width: 4p. The line segment that passes through the focus and it is perpendicular to the axis with endpoints on the parabola, is called the focal chord, and the focal width is the length of the focal chord.

Given equation

[tex]x^{2} =12y[/tex]

⇒ [tex](x-0)^{2}=12(y-0)[/tex]

Parabola vertex form with focus point distance

[tex](y-k)^{2}=4p(x-h)[/tex]

[tex](x-h)^{2}=4p(x-h)[/tex]

Vertex (h, k)

p = Distance from vertex to focus or directrix

4p = focal width

[tex]h = 0, k = 0,4p=12[/tex]

Hence, length of focal width is 12

Find out more information about focal width here

https://brainly.com/question/1832455

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