The circle C, with centre at the point A, has equation x2 + y2 – 10x + 9 = 0. Find
(a) the coordinates of A, (2)
(b) the radius of C, (2)
(c) the coordinates of the points at which C crosses the x-axis. (2)
Given that the line l with gradient is a tangent to C, and that l touches C at the point T,
(d) find an equation of the line which passes through A and T. (3)

Key features: the functions can not be parallels, this means that their respective slopes can not be equal or multiple to the other

Step-by-step explanation:

Take for instance 2 linear functions,  and

If they intersect in some point in the space, say that is

Then (x1,y1)=(x3,y3), (x2.y2)= (x3,y3)

So, we can compare the two functions and get the following result;

It tells us that if M=m, we get an error, meaning that the functions are in fact parallels and there is no way that they meet in some point.

hope this helps!