couldn't understand the whole part beneath the y=4/3x - 10/3 .........

Basically you have 3 unknowns to solve for, namely r, x- and y-coordinate of the intersection. So you need to form 3 eqns to solve.

First eqn I used what was given to me. 3rd eqn is your typical eqn of circle. The 2nd one is obtained using the fact that radius is perpendicular to tangent (angle properties of circles).

ohoh I see....
but the 2nd equation you write ( Let pt of intersection be (a,b) ) I don't understand this part.

Point where the tangent touches the circle

how to get b-2/a+1 = -3/4........