If A = {x2 + y2 = 16} and B = {9x2 + 25y2 = 225}.Then n(A ∩ B) is equal to

The given sets A and B represent two equations of circle and ellipse respectively.

Set A: x^2 + y^2 = 16 is a circle with center at origin and radius 4.

Set B: 9x^2 + 25y^2 = 225 is an ellipse with center at origin and semi-major axis a = 5 and semi-minor axis b = 3.

The intersection of these two sets A and B would be the points that satisfy both equations.

To find the intersection, we can substitute y^2 from the first equation into the second equation:

9x^2 + 25(16 - x^2) = 225 9x^2 + 400 - 25x^2 = 225 16x^2 = 175 x^2 = 175/16 x = ± √(175/16)

Substitute x into the first equation to find y:

y^2 = 16 - x^2 y = ± √(16 - 175/16)

So, the intersection points are (± √(175/16), ± √(16 - 175/16)).

Therefore, the number of elements in the intersection of sets A and B, n(A ∩ B), is 4.