Given:
The condition is
![\[{{y}^{2}}~=\text{ }10x\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-9c17a3f9f3bb7ed247b77aed6ddface4_l3.png "Rendered by QuickLaTeX.com")
.
Here we realize that the coefficient of
![\[x\text{ }is\text{ }positive\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-1501025ffbb5e85dd45b087ff8d1dd03_l3.png "Rendered by QuickLaTeX.com")
.
Along these lines, the parabola opens towards right .
On contrasting this condition and
![\[{{y}^{2}}~=\text{ }4ax\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-0db40a32529e4cb09faf35480ee1d079_l3.png "Rendered by QuickLaTeX.com")
, we get,
![\[\begin{array}{*{35}{l}} 4a\text{ }=\text{ }10 \\ a\text{ }=~10/4\text{ }=\text{ }5/2 \\ \end{array}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-30857a546eabfba81757991d059bfaf8_l3.png "Rendered by QuickLaTeX.com")
Accordingly, the co-ordinates of the concentration
![\[=\text{ }\left( a,0 \right)\text{ }=\text{ }\left( 5/2,\text{ }0 \right)\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-3b5bf0dfda8ec8c547144a23f0adbf6f_l3.png "Rendered by QuickLaTeX.com")
Since, the given condition includes
![\[{{y}^{2}}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-e89bfe389513847bf1aaed2fed294b93_l3.png "Rendered by QuickLaTeX.com")
, the axis of the parabola is the
![\[x-axis\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-10f8e73a8537bcb6a398489836795e56_l3.png "Rendered by QuickLaTeX.com")
.
∴ The condition of directrix,
![\[x\text{ }=-a\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-194cfc80a593c24fb7ff6f14ee10a093_l3.png "Rendered by QuickLaTeX.com")
, then, at that point,
![\[x\text{ }=\text{ }\text{ }5/2\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-9d98a07cb03da3391928b4f78ad0b2ae_l3.png "Rendered by QuickLaTeX.com")
Length of latus rectum
![\[=\text{ }4a\text{ }=\text{ }4\left( 5/2 \right)\text{ }=\text{ }10\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-dc250e5b0b7172b29959817aa5adcfad_l3.png "Rendered by QuickLaTeX.com")
