a.math題一問 !

the things below are my questions.
Thank you very much for your help!


2007年CE paper (no.15):
A straight line L1:y=2x intersects a circle C at two points to form a
chord of length 8√5 .
Let P(a,b) and r be the center and radius of C respectively
(a)by considering the distance from P to L1 , or otherwise , show that
r^2=(4a^2-4ab+b^2+400)/5
I want to ask how to know the distance from P to L1 ?



2007年CE paper (no.10):
Let f(x) be a function of x .the graph of y=f’(x) which is a straight
line with x- and y-intercepts 4 and 2 respectively.
(a)Find the slope of tangent to the curve y=f(x) at x=1



2007年CE paper (no.8):
OCA is a straight line and BC┴OA . It is given that OA=6i+3j and
OB=2i+6j.
Let OC=k OA
(b)Find the value of k (I also want to know: how to find the
value of i and j .



2007年CE paper (no.9):
two rods HA and HB , each of length 5 m, are hinged at H. The rods
slide such that A,B,H are on the same vertical plane and A ,B move in
opposite direction on the horizontal floor.
Let AB be x m and the distance of H from the floor be y m.
(b.)When H is 3 m from the ground, its falling speed is 2ms^-1.Find
the rate of change of the distance between A and B with respect to
time at that moment.
(I don’t know why x/2*dx/dt+2y*dy/dt=0 and dy/dt=-2)



2007年CE paper (no.3):
find the general solution of the equation cosx- √2cos2x + cos3x=0