Thank you for reporting, we will resolve it shortly
Q.
The eccentricity of the ellipse represented by the equation $25x^{2} + 16y^{2} - 150x - 175 = 0$ is
Conic Sections
Solution:
The given equation is
$25\left(x^{2} - 6x\right) + 16\left(y^{2}\right) = 175$
$\Rightarrow \, 25\left(x - 3\right)^{2} + 16\left(y - 0\right)^{2} = 400$
$\Rightarrow \, \frac{\left(x-3\right)^{2}}{16}+\frac{\left(y-0\right)}{25}=1$
The major axis of this ellipse is a line parallel to the $y$-axis i.e. $x = 3$. Therefore, its eccentricity is given by
$e=\sqrt{1-\frac{a^{2}}{b^{2}}}=\sqrt{1-\frac{16}{25}}=\frac{3}{5}\cdot$