Why do they intersect so much?

This is a very simple question.
It has three cases:

$Case-I$ : Two circles cut each other.
The maximum number of intersection points is 2 .
Therefore, $\dbinom 42 \times 2 = 12$ [ Since we have to select any two circles and then each such pair have two intersection points]

$Case-II$ : Two parabolas cut each other.
The maximum number of intersection points is 4 .
Therefore, $\dbinom 42 \times 4 = 24$ [ Since we have to select any two parabolas and then each such pair have four intersection points]

$Case-III$ : One circle and on parabola cut each other.
The maximum number of intersection points is 2 .
Therefore, $\dbinom 41\times \dbinom 41 \times 4 = 64$ [ Since we have to select any one circle and one parabola and then each such pair have four intersection points]

Thus , total number of intersection points is $12+24+64=\boxed{100}$