Show why the lines do not intersect

y = 2x + 4

y = x² - 4

Find the coordinates of the mid-point of the line AB where A and B are the points where the line y = 2x + 4 and the curve y = x - 4 intersect

Find:

a) the equation of the straight line passing through the point (9,4) and which is perpendicular to the line y = 3x - 3

b) where this line cuts the line y = 3x - 3

c) the perpendicular distance from (9,4) to the line y = 3x -3

The curves y = 2x² - 3x and y = x² intersect at two points. Find the equation of the straight line joining these points.

The line y = ax - 1 and the curve y = x² + bx -5 intersect at the points P(4, -5) and Q. Find the values of a and b and the coordinates of Q.

*Please show the working so I can learn from it! Thank you in advance to anyone that helps :-)

Any help is of course appreciated, please answer as much as you can!