The curve represented by the equation \( \dfrac{x^{2}}{\sin \sqrt{2}-\sin \sqrt{3}}+\dfrac{y^{2}}{\cos \sqrt{2}-\cos \sqrt{3}}=1 \) is

sin sqrt2 - sin sqrt3 = 2cos((sqrt2+sqrt3)/2)sin((sqrt2-sqrt3)/2); (sqrt2+sqrt3)/2=1.573>pi/2 so both factors negative, giving a small positive value (~0.0007). cos sqrt2 - cos sqrt3 = 0.156+0.160 ~ 0.317 > 0. Both denominators positive: ellipse, and the y^2 denominator is larger, so major axis and foci on the y-axis.