Find the coordinates of the foci, the vertices, the length of major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse. \[{{x}^{2}}/100\text{ }+\text{ }{{y}^{2}}/400\text{ }=\text{ }1\]

Home » Find the coordinates of the foci, the vertices, the length of major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse.

Find the coordinates of the foci, the vertices, the length of major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse.

${{x}^{2}}/100\text{ }+\text{ }{{y}^{2}}/400\text{ }=\text{ }1$

Find the coordinates of the foci, the vertices, the length of major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse.

${{x}^{2}}/100\text{ }+\text{ }{{y}^{2}}/400\text{ }=\text{ }1$

Given:

The condition is

${{x}^{2}}/100\text{ }+\text{ }{{y}^{2}}/400\text{ }=\text{ }1$

Here, the denominator of

${{y}^{2}}/400$

is more noteworthy than the denominator of

${{x}^{2}}/100$

.

Thus, the significant pivot is along the $y-axis$ , while the minor hub is along the $x-axis$ .

On contrasting the given condition and

${{x}^{2}}/{{b}^{2}}~+\text{ }{{y}^{2}}/{{a}^{2}}~=\text{ }1$

, we get

$\begin{array}{*{35}{l}} b\text{ }=\text{ }10\text{ }and\text{ }a\text{ }=20. \\ c\text{ }=\text{ }\surd \left( {{a}^{2}}~\text{ }{{b}^{2}} \right) \\ =\text{ }\surd \left( 400-100 \right) \\ =\text{ }\surd 300 \\ =\text{ }10\surd 3 \\ \end{array}$