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$\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1\]has its foci at $(0,\pm 4)$

$\frac{x^2}{a^2}-\frac{y^2}{b^2} = 1\]has its foci at $(\pm 6,0).$

Find  l ab l

The first equation is an ellipse  with its center at (0, 0) and its major axis along y 

The equation for the focus  is    (0 , 0 ± c)  where  c = ±4

And we have that   a^2 - b^2  = c^2  ⇒  a^2 - b^2  = 16   (1)

The second equation is a hyperbola with its center at (0, 0)  and its major axis along x

The equation for the focus is  (0 ± c, 0)  where c = ±6

And we  have that a^2 + b^2  = c^2  ⇒  a^2 + b^2 =  36   (2)

Add  (1) and (2)   and we have that

2a^2  =  52

a^2  =  26   ⇒    a =  ±√26

And  using (2)

26 + b^2  = 36

b^2  =  10 ⇒  b = ±√10  

So

l ab l  =  l √26 * √10 l  =   l √ 2 * √13 * √2 * √5  l  =    2√65