We realize that the beginning of the facilitate plane is taken at the vertex of the curve, where its upward pivot is along the positive
Diagrammatic portrayal is as per the following:
The condition of the parabola is of the structure
![\[{{x}^{2}}~=\text{ }4ay~\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-e429ca790b3516698d1c41879cc92db9_l3.png "Rendered by QuickLaTeX.com")
(as it is opening upwards).
It is given that at base curve is
![\[10m\text{ }high\text{ }and\text{ }5m\text{ }wide.\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-40bb0c000deac2963c647f04654ea939_l3.png "Rendered by QuickLaTeX.com")
In this way,
![\[y\text{ }=\text{ }10\text{ }and\text{ }x\text{ }=\text{ }5/2\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-f242d54f806a0b8c788f86be5db1777a_l3.png "Rendered by QuickLaTeX.com")
from the above figure.
Unmistakably the parabola goes through point
![\[\left( 5/2,\text{ }10 \right)\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-62b5a5d22d658777e89d099b3aa2b7f6_l3.png "Rendered by QuickLaTeX.com")
![\[<span class="ql-right-eqno"> (1) </span><span class="ql-left-eqno"> </span><img src="https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-593ad01ad2c50f3aee20d7004bb35e9f_l3.png" height="167" width="258" class="ql-img-displayed-equation quicklatex-auto-format" alt="\begin{align*} & \begin{array}{*{35}{l}} So,\text{ }{{x}^{2}}~=\text{ }4ay \\ {{\left( 5/2 \right)}^{2}}~=\text{ }4a\left( 10 \right) \\ \end{array} \\ & \begin{array}{*{35}{l}} 4a\text{ }=\text{ }25/\left( 4\times 10 \right) \\ a=\text{ }5/32 \\ \end{array} \\ \end{align*}" title="Rendered by QuickLaTeX.com"/>\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-ff4ac20c9a32b77b9dca73c69272fd46_l3.png "Rendered by QuickLaTeX.com")
we realize the curve is as a parabola whose condition is
![\[~{{x}^{2}}~=\text{ }5/8y\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-410ab9cfa141cd9f245d59ee355d4507_l3.png "Rendered by QuickLaTeX.com")
We need to discover width, when stature
![\[=\text{ }2m.\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-130764126c132eb9fecb7fa0c6d322aa_l3.png "Rendered by QuickLaTeX.com")
To discover
![\[x,\text{ }when\text{ }y\text{ }=\text{ }2.\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-a9bc0d592038e281f24b49380e3a2e22_l3.png "Rendered by QuickLaTeX.com")
At the point when,
![\[y\text{ }=\text{ }2,\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-2cf7245d4ec40cc96a55059338daa7ed_l3.png "Rendered by QuickLaTeX.com")
![\[<span class="ql-right-eqno"> (2) </span><span class="ql-left-eqno"> </span><img src="https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-4610f3449fd3eeee50e6963d4c3c47ae_l3.png" height="284" width="304" class="ql-img-displayed-equation quicklatex-auto-format" alt="\begin{align*} & {{x}^{2}}~=\text{ }5/8\text{ }\left( 2 \right) \\ & \begin{array}{*{35}{l}} =\text{ }5/4 \\ x\text{ }=\text{ }\surd \left( 5/4 \right) \\ =\text{ }\surd 5/2 \\ AB\text{ }=\text{ }2\text{ }\times \text{ }\surd 5/2m \\ =\text{ }\surd 5m \\ =\text{ }2.23m\text{ }\left( approx. \right) \\ \end{array} \\ \end{align*}" title="Rendered by QuickLaTeX.com"/>\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-fbd4ba3f1693cc3f010c27dc8cdc74f7_l3.png "Rendered by QuickLaTeX.com")
Subsequently, when the curve is
![\[2m\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-06cda4dd4cc328d3b1dd3ec6463009fd_l3.png "Rendered by QuickLaTeX.com")
from the vertex of the parabola, its width is roughly
![\[2.23m.\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-424df022f4a5bd75d0de924914d7968d_l3.png "Rendered by QuickLaTeX.com")