Coordinate Geometry?

[Panda]

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!

[stapel_eliz]

Actually, we need to see your working, so we can determine where you're needing help. Or are you first needing lessons, so you have some idea what is being asked of you?

[Panda]

I'm needing lessons, really. I'd like to gather an understanding through a few worked examples as a basis, please help as much as you can, any input is greatly appreciated!

[stapel_eliz]

These questions cover a semester or so of material, so you have a lot of self-study to do. (Enrolling in a course would probably be better.) You'll need to study at least the following:

Solving Linear Equations
Solving Quadratic Equations
Solving Systems of Non-Linear Equations
Solving Systems of Linear Equations
The Slope of a Straight Line
Straight-Line Equations
The Distance Formula
The Midpoint Formula

The above should suffice to get you started. (Solutions won't make sense until you know what's going on, anyway.) Please allow at least a few days, if not a couple weeks, to study the above, along with any linked material that you also need to learn.

[Panda]

Thank you very much for the links, I shall definitely be using them. Thanks again! :-)