Leave
![\[A\text{ }and\text{ }B\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-7749aa70ac649e4d504c4b4befc094fc_l3.png "Rendered by QuickLaTeX.com")
alone the places of the two banner posts and
![\[P\left( x,\text{ }y \right)\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-cd883200d1efccdae2a63a5fdacbf098_l3.png "Rendered by QuickLaTeX.com")
be the situation of the man.
In this way,
![\[PA\text{ }+\text{ }PB\text{ }=\text{ }10.\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-166b130d7962ec3d5b61957eef394e71_l3.png "Rendered by QuickLaTeX.com")
We realize that if a point moves in plane so that the amount of its separation from two fixed point is steady, then, at that point, the way is a circle and this consistent worth is equivalent to the length of the significant hub of the oval.
Then, at that point, the way depicted by the man is a circle where the length of the significant hub is
![\[10m\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-07dcee05ecc28021aa8fe4d9036bb600_l3.png "Rendered by QuickLaTeX.com")
, while focuses
are the foci.
Presently let us take the beginning of the facilitate plane as the focal point of the circle, and taking the significant hub along the
![\[x-pivot,\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-ed13061f8476481bf8a3f697be1e8a1b_l3.png "Rendered by QuickLaTeX.com")
The diagrammatic portrayal of the oval is as per the following:
The condition of the oval is as
![\[{{x}^{2}}/{{a}^{2}}~+\text{ }{{y}^{2}}/{{b}^{2}}~=\text{ }1\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-30ca1b241e18b8ec64629e47f8d414c3_l3.png "Rendered by QuickLaTeX.com")
, where ‘
![\[a\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-a3ab43dca3872e69a0c1be257c1ecec8_l3.png "Rendered by QuickLaTeX.com")
‘ is the semi-significant hub.
Thus,
![\[2a\text{ }=\text{ }10\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-8492684ed8d0a6aa9e15991e738d641d_l3.png "Rendered by QuickLaTeX.com")
![\[\begin{array}{*{35}{l}} a\text{ }=\text{ }10/2 \\ =\text{ }5 \\ \end{array}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-5390eadef56f8503614a6c39510ac96f_l3.png "Rendered by QuickLaTeX.com")
Distance between the foci
![\[2c\text{ }=\text{ }8\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-0f307aa0d2f601084cbc4d2f0ca72601_l3.png "Rendered by QuickLaTeX.com")
![\[\begin{array}{*{35}{l}} c\text{ }=\text{ }8/2 \\ =\text{ }4 \\ \end{array}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-954093dd762404edae2c7669e6085107_l3.png "Rendered by QuickLaTeX.com")
By utilizing the connection,
![\[c\text{ }=~\surd ({{a}^{2}}~\text{ }{{b}^{2}})\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-c7d6dcc3657617e24094e23a193017b7_l3.png "Rendered by QuickLaTeX.com")
,we get
![\[<span class="ql-right-eqno"> (1) </span><span class="ql-left-eqno"> </span><img src="https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-457ca8b04f343b7a18bcb9d57531a779_l3.png" height="198" width="215" class="ql-img-displayed-equation quicklatex-auto-format" alt="\begin{align*} & 4\text{ }=~\surd \left( 25\text{ }\text{ }{{b}^{2}} \right) \\ & \begin{array}{*{35}{l}} 16\text{ }=\text{ }25\text{ }\text{ }{{b}^{2}} \\ {{b}^{2}}~=\text{ }25\text{ }-1 \\ =\text{ }9 \\ b\text{ }=\text{ }3 \\ \end{array} \\ \end{align*}" title="Rendered by QuickLaTeX.com"/>\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-f79809150a43874087a37be9024111ee_l3.png "Rendered by QuickLaTeX.com")
Henceforth, condition of the way followed by the man
![\[{{x}^{2}}/25\text{ }+\text{ }{{y}^{2}}/9\text{ }=\text{ }1\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-9b81550b718879c6bec3db2fd952207c_l3.png "Rendered by QuickLaTeX.com")