new to cirlces and getting stumped at this question. I'll run through my workings and thoughts - any advise would be greatly received.

The equation of a cirlce with centre C is: $\displaystyle (x-3)^2+ (y-4)^2 = 9$ and O is the origin. the line joining O and C can be extended to meet the cirlce at P. Find the coordinates of P and show the equation of the tangent to the cirlce at P is $\displaystyle 3x + 4y = 40$.

So, I can observe the coords at C to be (3,4) and the line OP to have an equation of $\displaystyle y-0 = \frac{4}{3}(x-0)$ and therefore, $\displaystyle y=\fra{4}{3}x$.

Substitute this into the circle equation and I get $\displaystyle 75x^2 + 576x -108 = 0$ which solves to be approx. x = 0.1831 and -7.8631

But these x coords cant be right as I know the circle lies in the 1st quadrant and there for cannot have an intercept with the line at x = -7.8....

What has gone wrong? Once I get the coords for the point P I can calculate the new equation of the line.