An arch is in the form of a semi-ellipse. It is 8 m wide and 2 m high at the centre. Find the height of the arch at a point 1.5 m from one end.
An arch is in the form of a semi-ellipse. It is 8 m wide and 2 m high at the centre. Find the height of the arch at a point 1.5 m from one end.

Since, the tallness and width of the circular segment from the middle is

    \[2m\text{ }and\text{ }8m\]

separately, obviously the length of the significant hub is

    \[8m\]

, while the length of the semi-minor hub is

    \[2m.\]

The beginning of the organize plane is taken as the focal point of the oval, while the significant pivot is brought the

    \[x-hub\]

.

Consequently, Diagrammatic portrayal of semi-circle is as per the following:

NCERT Solutions for Class 11 Maths Chapter 11 – Conic Sections image - 4

The condition of the semi – ellipse will be of the from

    \[x2/16\text{ }+\text{ }y2/4\text{ }=\text{ }1,\text{ }y\text{ }\ge \text{ }0\text{ }\ldots \text{ }(1)\]

Leave An alone a point on the significant hub with the end goal that

    \[AB\text{ }=\text{ }1.5m.\]

Presently draw

    \[AC\bot OB.\]

    \[OA\text{ }=\text{ }\left( 4\text{ }\text{ }1.5 \right)m\text{ }=\text{ }2.5m\]

The x – coordinate of point

    \[C\text{ }is\text{ }2.5\]

On subbing the worth of

    \[x\text{ }with\text{ }2.5\]

in condition

    \[\left( 1 \right),\]

we get,

    \[<span class="ql-right-eqno"> (1) </span><span class="ql-left-eqno">   </span><img src="https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-fb08726048063e3e2fe8be83f4395249_l3.png" height="284" width="326" class="ql-img-displayed-equation quicklatex-auto-format" alt="\begin{align*} & \begin{array}{*{35}{l}} {{\left( 2.5 \right)}^{2}}/16\text{ }+\text{ }{{y}^{2}}/4\text{ }=\text{ }1  \\ 6.25/16\text{ }+\text{ }{{y}^{2}}/4\text{ }=\text{ }1  \\ {{y}^{2}}~=\text{ }4\text{ }\left( 1\text{ }\text{ }6.25/16 \right)  \\ \end{array} \\ & \begin{array}{*{35}{l}} =\text{ }4\text{ }\left( 9.75/16 \right)  \\ =\text{ }2.4375  \\ y\text{ }=\text{ }1.56\text{ }\left( approx. \right)  \\ So,\text{ }AC\text{ }=\text{ }1.56m  \\ \end{array} \\ \end{align*}" title="Rendered by QuickLaTeX.com"/>\]

Consequently, the stature of the curve at a point

    \[1.5m\]

from one end is roughly

    \[1.56m.\]