Find the length of the latus rectum of the following ellipse: 25x^2 + 9y^2 - 300x - 144y + 1251 = 0.

$25x^2 + 9y^2 - 300x - 144y + 1251 = 0$   ←   ellipse

$25(x^2 - 12x) + 9(y^2 - 16y) = -1251$

$25(x^2 - 12x + 36) + 9(y^2 - 16y + 64) = -1251 + 25(36) + 9(64)$

$25(x - 6)^2 + 9(y - 8)^2 = 225$

$\dfrac{(x - 6)^2}{9} + \dfrac{(y - 8)^2}{25} = 1$
 

$a^2 = 25$   →   $a = 5$

$b^2 = 9$   →   $b = 3$
 

$LR = \dfrac{2b^2}{a} = \dfrac{2(9)}{5} = 3.6$