(i)
![\[4{{x}^{2}}~+\text{ }3{{y}^{2}}~=\text{ }1\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-a633e2aeba83e4a13d29f6a0ebf54e92_l3.png "Rendered by QuickLaTeX.com")
Given:
The equation of ellipse
![\[=>\text{ }4{{x}^{2}}~+\text{ }3{{y}^{2}}~=\text{ }1\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-f4491b73e7b85c87972ac734d63cb065_l3.png "Rendered by QuickLaTeX.com")
This equation can be expressed as
By using the formula,
Eccentricity:
Here,
![\[{{a}^{2}}~=\text{ }1/4\text{ }and\text{ }{{b}^{2}}~=\text{ }1/3\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-844a104367b79d4290250c260adf8af2_l3.png "Rendered by QuickLaTeX.com")
Length of latus rectum
![\[=\text{ }2{{b}^{2}}/a\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-47c6e5dfc4ff2158af570ee22ebe4b2a_l3.png "Rendered by QuickLaTeX.com")
![\[=\text{ }\left[ 2\left( 1/4 \right) \right]\text{ }/\text{ }\left( 1/\surd 3 \right)\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-3aa375b0206bb10060b66561f1b30c61_l3.png "Rendered by QuickLaTeX.com")
![\[=~\surd 3/2\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-f7f3577ed67ee943b8254682bc4f6f0e_l3.png "Rendered by QuickLaTeX.com")
Coordinates of foci
![\[\left( \pm ae,\text{ }0 \right)\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-d3cb528ebfdb03c275158177df0f88e4_l3.png "Rendered by QuickLaTeX.com")
(ii)
![\[25{{x}^{2}}~+\text{ }16{{y}^{2}}~=\text{ }1600\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-c5e91e549f47032a773b413936a17b6e_l3.png "Rendered by QuickLaTeX.com")
Given:
The equation of ellipse
![\[=>\text{ }25{{x}^{2}}~+\text{ }16{{y}^{2}}~=\text{ }1600\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-ffcb1709b3368bc6cd05437cd4d6f4ac_l3.png "Rendered by QuickLaTeX.com")
This equation can be expressed as
By using the formula,
Eccentricity:
Here,
![\[{{a}^{2}}~=\text{ }64\text{ }and\text{ }{{b}^{2}}~=\text{ }100\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-94a907d29458c30dac0e6ab4f99e3290_l3.png "Rendered by QuickLaTeX.com")
Length of latus rectum
![\[=\text{ }\left[ 2\left( 64 \right) \right]\text{ }/\text{ }\left( 100 \right)\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-dd0db9b5d899bfb80c7e8690a2daf5b6_l3.png "Rendered by QuickLaTeX.com")
![\[=\text{ }32/25\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-3c4c49658c4ed5e2bfe13d764674851b_l3.png "Rendered by QuickLaTeX.com")
Coordinates of foci
