Find the equation for the ellipse that satisfies the given conditions: Length of major axis $= 26$,foci $= (\pm 5, 0)$.
(N/A) The length of the major axis is $2a = 26$,which gives $a = 13$.
The foci are given as $(\pm 5, 0)$,which implies $c = 5$ and the major axis lies along the $x$-axis.
The standard equation of the ellipse is $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$.
Using the relation $a^2 = b^2 + c^2$,we have $13^2 = b^2 + 5^2$.
$169 = b^2 + 25 \Rightarrow b^2 = 144$.
Substituting the values of $a^2$ and $b^2$ into the standard equation,we get $\frac{x^2}{169} + \frac{y^2}{144} = 1$.
The foci are given as $(\pm 5, 0)$,which implies $c = 5$ and the major axis lies along the $x$-axis.
The standard equation of the ellipse is $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$.
Using the relation $a^2 = b^2 + c^2$,we have $13^2 = b^2 + 5^2$.
$169 = b^2 + 25 \Rightarrow b^2 = 144$.
Substituting the values of $a^2$ and $b^2$ into the standard equation,we get $\frac{x^2}{169} + \frac{y^2}{144} = 1$.
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