How Do You Solve Challenging A Level C2 Maths Problems?

[THC_addict]

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.
Thanks in advance.

Homework Statement

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.

Homework Equations

Find the equation of the circle.

The Attempt at a Solution

Well, i did try, but i don't 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 can't get any further.
I think i have to find the centre and the radius and that will give me the circle's equation, please help.

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
=)

 

[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=$\sqrt{f^2+g^2-c}$

 

[THC_addict]

Thanks man. that equation helped. its not on the formula sheet of the past papers so ill have to memorise that for tommorows test.

EDIT: Yah, and i figured out a way to do the second one too.
Thanks