Why do we need 4 points for homography but 7/8 points for fundamental matrix calculation? Sorry if this is a trivial question but I could not find a suitable answer elsewhere. 

I recently learned about homography and fundamental matrices in a CV class. I understand how these matrices are calculated and how the the formulae are derived. I also understand that both homography and fundamental matrices have 8 degrees of freedom.

But I'm unable to understand why we need 4 point correspondences for finding the homography while 8 points for calculating the fundamental matrix. 

Shouldn't the number of correspondences needed be same intuitively?
It is because in the case of fundamental matrix, each correspondence point relates to only one constraint(i.e it maps a point to a line in other image). Hence 8 correspondence points are required. 

But in the case of homography, each correspondence solves two constraints. Hence only 4 correspondence points are sufficient.