Is the distance around the earth same at different latitudes?

Of course. The further away from the equator, the smaller the circle..or distance. The largest distance is always the equator...as this is the largest circumferance.

from Newton.org....

"The circumference is given by 2 times pi times the radius, where pi is 3.14. The radius of the earth at the equator is about 6378 kilometers so the distance around the earth at the equator is 2 time 3.14 times 6378 which equals 40,074 kilometers. "