• # question_answer The length of major axis of ellipse is 26 and its foci is $\left( \pm \text{ }\mathbf{5},\mathbf{0} \right)$ then equation of ellipse be A)  $\frac{{{x}^{2}}}{144}+\frac{{{y}^{2}}}{169}=1$ B)         $\frac{{{x}^{2}}}{169}-\frac{{{y}^{2}}}{144}=-1$ C)  $\frac{{{x}^{2}}}{169}+\frac{{{y}^{2}}}{144}=-1$           D)  $-\frac{{{x}^{2}}}{169}-\frac{{{y}^{2}}}{144}=-1$

[c] $\because 2a=26~~~a\Rightarrow 13.$ foci$=\left( \pm 5,0 \right)$ $\therefore a.e=5\Rightarrow e=\frac{5}{a}=\frac{5}{13}$ $\therefore {{b}^{2}}={{a}^{2}}(1-{{e}^{2}})=169{{\left[ 1-\left( \frac{25}{13} \right) \right]}^{2}}$ $=169\times \frac{144}{169}=144.$ hence the equation of ellipse be  $\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}=1\Rightarrow \frac{{{x}^{2}}}{169}+\frac{{{y}^{2}}}{144}=1$ Hence, Option [b] is correct