Homework Help: Need help with A level C2 maths

1. Jan 27, 2008

Hi, i think this is the place for this type of questions? If not, please move it.

I need help with these type of questions, i am not being able to do them.
Theyre from Edexcel Pure mathematics C1 and C2.

1. The problem statement, all variables and given/known data

AB is a chord of a circle where A is at (1,3) and B is at (4,4).
The tangent to the circle at A is the line y= 2x + 1.

2. Relevant equations

Find the equation of the circle.

3. The attempt at a solution

Well, i did try, but i dont know how to do this stuff.
I found the gradient of the normal then found the normals equation using
y - y1 = m(x - x1)
but cant get any further.

Also, i need help with these type of questions:

The point (6,1) lies on the circle x^2 - y^2 - 8x - 4y + 15 = 0

Find the coordinates of the second point at which the normal cuts the circle.

How the hell do you do that? It gives a hint, "draw a sketch"

Thanks
=)

2. Jan 27, 2008

rock.freak667

First one I can think of one way to find it but that may be too tedious to do it out. But it all begins with the general equation of a circle.

General equation of a circle is:

$$x^2+y^2+2fx+2gy+c=0$$

Centre=(-f,-g) and radius=$\sqrt{f^2+g^2-c}$

3. Jan 27, 2008