Find the equation of the ellipse whose foci are at \[\left( \pm \mathbf{1},\text{ }\mathbf{0} \right)\] and e=1/2

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Find the equation of the ellipse whose foci are at

$\left( \pm \mathbf{1},\text{ }\mathbf{0} \right)$

and e=1/2

CBSE | Class 11 | Ellipse | Maths | RS Aggarwal

Find the equation of the ellipse whose foci are at

$\left( \pm \mathbf{1},\text{ }\mathbf{0} \right)$

and e=1/2

Let the equation of the required ellipse be

$\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}=1$

Given:

Coordinates of foci =

$\left( \pm 1,\text{ }0 \right)$

…(i)

We know that,

Coordinates of foci =

$\left( \pm c,\text{ }0 \right)$

…(ii)

∴ From eq. (i) and (ii), we get

c =

$1$

It is also given that

we know that,

⇒ a =

$2$

Now, we know that,

$\begin{array}{*{35}{l}} {{c}^{2}}=\text{ }{{a}^{2}}\text{ }{{b}^{2}} \\ \Rightarrow {{\left( 1 \right)}^{2}}=\text{ }{{\left( 2 \right)}^{2}}\text{ }{{b}^{2}} \\ \Rightarrow 1\text{ }=\text{ }4\text{ }\text{ }{{b}^{2}} \\ \Rightarrow {{b}^{2}}=\text{ }4\text{ }\text{ }1 \\ \Rightarrow {{b}^{2}}=\text{ }3 \\ \end{array}$