Question

Find the equation for the ellipse that satisfies the given conditions,
Length of major axis 26, foci $(\pm 5,0)$

Answer 1

The foci $(\pm 5,0)$ lie on x - axis .
So the equation of ellipse in standard form is,
$\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\text{Now length of major axis 2a = 26}\Rightarrow a=13\text{Foci}(\pm c,0)\text{is}(\pm 5,0)\Rightarrow c=5\text{We know that}{c}^2=a^2-b^2\therefore (5{)}^2=(13{)}^2-b^2\Rightarrow b^2=169-25=144\text{Thus equation of required ellipse is},\frac{x^2}{169}+\frac{y^2}{144}=1.$