![\[\left( \pm \mathbf{1},\text{ }\mathbf{0} \right)\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-873e68902b5445bb221bebb969489511_l3.png "Rendered by QuickLaTeX.com")
Let the equation of the required ellipse be
![\[\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}=1\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-d32e615a6517b76e65b04fd25ae8bf0a_l3.png "Rendered by QuickLaTeX.com")
Given:
Coordinates of foci =
![\[\left( \pm 1,\text{ }0 \right)\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-a2b7b328e6d28ba9482ee020e190b1c5_l3.png "Rendered by QuickLaTeX.com")
…(i)
We know that,
Coordinates of foci =
![\[\left( \pm c,\text{ }0 \right)\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-50136607b1975cc7b38f263e2c84d025_l3.png "Rendered by QuickLaTeX.com")
…(ii)
∴ From eq. (i) and (ii), we get
c =
![\[1\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-64318110f3a374fb786ef713c0b0c575_l3.png "Rendered by QuickLaTeX.com")
It is also given that
we know that,
⇒ a =
![\[2\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-b1e8e3db630df9050b1fec3c4066d5e6_l3.png "Rendered by QuickLaTeX.com")
Now, we know that,
![\[\begin{array}{*{35}{l}} {{c}^{2}}=\text{ }{{a}^{2}}\text{ }{{b}^{2}} \\ \Rightarrow {{\left( 1 \right)}^{2}}=\text{ }{{\left( 2 \right)}^{2}}\text{ }{{b}^{2}} \\ \Rightarrow 1\text{ }=\text{ }4\text{ }\text{ }{{b}^{2}} \\ \Rightarrow {{b}^{2}}=\text{ }4\text{ }\text{ }1 \\ \Rightarrow {{b}^{2}}=\text{ }3 \\ \end{array}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-e0e4122978ebbee25f12d74e2ccdc849_l3.png "Rendered by QuickLaTeX.com")
Substituting the value of
![\[{{a}^{2}}and\text{ }{{b}^{2}}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-f18222cca635e12bc75738380c9cc066_l3.png "Rendered by QuickLaTeX.com")
in the equation of an ellipse, we get Downloaded from
![\[\frac{{{x}^{2}}}{4}+\frac{{{y}^{2}}}{3}=1\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-b1ca48639234e861da902f0ecd3b138a_l3.png "Rendered by QuickLaTeX.com")