I'm a Year 11 Geometry & Trigonometry student in Australia. I've never really had many problems with this subject, and I get a two page assignment and an hour long test every week, and an investigation every month, and am doing pretty well. But I just cannot work out the Investigation i've just been given. And its due monday. I've spent about 5 hours on it and I keep getting different answers and none of them work out.

1. Points P and C have position vectorspandcgiven byp= 9i+ 7jand 4i+ 2j.

A circle, with centre at point C cuts the x asis at the point with co-ordinates (10,0).

Find

(i) a vector equation of this circle.

This was fairly easy. |r- (4 2)|= root40. Am I correct?

Tangent lines from point P touch this circle at points A and B.This was easy too, root10 for both.

Find

(ii) the lengths, PA and PB, of the tangents.

(iii) vector equations for the tangent linesMy teacher says its better to do (iv) first, because then you know the direction of the two lines, hence you can work out the vector equations. But I have no idea how i'm supposed to go about it. I'm fairly sure it involves CA.PA=0, because it involves lines perpendicular to one another. And I ended up with:

(iv) the position vectors,aandb, of the points of contact A and B.

x^2 + y^2 -13x -9y + 50 = 0, then taking this equation away from the equation of the circle (x^2 + y^2 - 8x - 4y + 20 = 0).

Then the two x^2 + y^2's cancel and you can find y with some algebra, then you can put y back into the first equation to find x. But I keep getting weird things for x. I got 4 and thought it sounded ok, but my teacher says that the final answer for (iv) is (6 10), and (10 4). But I just can't get these.

Then to cap it all theres another really hard question.

2. In general, find an expression in terms ofAny help would be much appreciated. Thanks.p,candrfor the length of the tangents from any point P, external to a circle, with centre C and a radius r.