Preliminary Maths Questions (updated)

[hard.candy]

Hi, I need help with a few questions, any feedback would be greatly appreciated.

1. Determine the equation of the line through M(-1, 2) if M is the mid-point of the intercepts on the x-axis and y-axis.

2. Solve the inequation x² - 4>0 and hence state the domain of 5/√x² -4

3. set up a pair of simutaneous equations and hence solve the problem :
two people are 16km apart on a straight road. they start walking at the same time, If they walk towards each other they will meet in 2hrs but if they walk in the same direction (so that the distance between them is decreasing, they will meet in 8hrs. find their walking speeds.

thanks in advance for any help you can give.


4. solve the following for x and y given both are rational numbers
1½ + √x+2y = 3x+y+2/3√3

for this question i put the rhs in to y=mx+b form and got y= -3x - 2/3√3 and then subbed that into the left hand side. so i got 1½ +√x+2(-3x- 2/3√3)
then i expanded the bracket and got 1½ + √x-6x - 4/3√3 but from there i got lost, i couldnt find a way to get rid of the surds to make them rational numbers.

5. determine the length of the chord cut off from the line 2y -x +8 =0 by the circle (x+2)² + (y+3)² = 4.

i got that (-2, -3) is the centre of the circle and that its radius is two. i put the line in y= mx+b form and sub some values in for x and then my line ended up no where near my circle. is there an easier way to do this?


thanks again.