Where all my simps at and tell the truth

Select the sequences that are geometric.

Parabolas y=−2x^2 and y=2x^2 +k intersect at points a and b that are in the third and the fourth quadrants respectively. find k if length of the segment ab is 5.

X/y + 4y/x divided by x/y - 2y/x explain as in depth as you can how you simplfied the fractions. i don't know where to start on this : /