We realize that the vertex is at the absolute bottom of the link. The beginning of the facilitate plane is taken as the vertex of the parabola, while its upward hub is brought the positive
![\[y\text{ }\text{ }axis.\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-b98b0b509229d951366b88608a9bf9fe_l3.png "Rendered by QuickLaTeX.com")
Diagrammatic portrayal is as per the following:
Here,
![\[AB\text{ }and\text{ }OC\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-7e21f78ad3ff5dea3db9dca662c993db_l3.png "Rendered by QuickLaTeX.com")
are the longest and the most brief wires, separately, appended to the link.
DF is the supporting wire appended to the streets,
![\[18m\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-bf1031cb1e302e30cf30a3fc6b310aef_l3.png "Rendered by QuickLaTeX.com")
from the center.
Along these lines,
![\[AB\text{ }=\text{ }30m,\text{ }OC\text{ }=\text{ }6m,\text{ }and\text{ }BC\text{ }=\text{ }50m.\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-7c3c2a5c7f2b303a9aa554ca64d83ed6_l3.png "Rendered by QuickLaTeX.com")
The condition of the parabola is of the from
![\[{{x}^{2}}~=\text{ }4ay\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-01c1ff86810fd1884156b37dc80a3522_l3.png "Rendered by QuickLaTeX.com")
(as it is opening upwards).
The directions of point A are
![\[\left( 50,\text{ }30\text{ }-\text{ }6 \right)\text{ }=\text{ }\left( 50,\text{ }24 \right)\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-d12ca2d28abf66925901e439e688cec2_l3.png "Rendered by QuickLaTeX.com")
Since,
![\[A\left( 50,\text{ }24 \right)\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-5d3e4a1e3670d43bee21ec04e08edec3_l3.png "Rendered by QuickLaTeX.com")
is a point on the parabola.
![\[\begin{array}{*{35}{l}} {{y}^{2}}~=\text{ }4ax \\ {{\left( 50 \right)}^{2}}~=\text{ }4a\left( 24 \right) \\ a\text{ }=\text{ }\left( 50\times 50 \right)/\left( 4\times 24 \right) \\ =\text{ }625/24 \\ \end{array}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-206c46bf0224e1267436646a1e32afd0_l3.png "Rendered by QuickLaTeX.com")
Condition of the parabola,
![\[{{x}^{2}}~=\text{ }4ay\text{ }=\text{ }4\times \left( 625/24 \right)y\text{ }or\text{ }6{{x}^{2}}~=\text{ }625y\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-fe08ef2abc684bf5253cc2c500b1b6c5_l3.png "Rendered by QuickLaTeX.com")
The
![\[x\text{ }\text{ coordinate}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-3a7568d96467681d18bdaa6954c811d5_l3.png "Rendered by QuickLaTeX.com")
of point
![\[D\text{ }is\text{ }18.\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-8e056ffcb5813e1d9c20e3f185dd3db6_l3.png "Rendered by QuickLaTeX.com")
Henceforth, at
![\[x\text{ }=\text{ }18,\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-4b65843acc5f1c4f93e1ae2a25ce1264_l3.png "Rendered by QuickLaTeX.com")
![\[\begin{array}{*{35}{l}} 6{{\left( 18 \right)}^{2}}~=\text{ }625y \\ y\text{ }=\text{ }\left( 6\times 18\times 18 \right)/625 \\ =\text{ }3.11\left( approx. \right) \\ Thus,\text{ }DE\text{ }=\text{ }3.11\text{ }m \\ DF\text{ }=\text{ }DE\text{ }+EF\text{ }=\text{ }3.11m\text{ }+6m\text{ }=\text{ }9.11m \\ \end{array}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-e65aa5dbf61239de747250fa256b06ef_l3.png "Rendered by QuickLaTeX.com")
Hence, the length of the supporting wire attached to the roadway
from the middle is approximately
![\[9.11m.\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-33a4592ba9a2538e84123fdf55364a60_l3.png "Rendered by QuickLaTeX.com")