Find an equation of the tangent to the circle with equation $x^2+y^2-10x+4y+4=0$ at the point $(2,2)$
I have solved up to $4y - 8 = 3x - 6$, but I am not sure whether the final answer should be $3x-4y+2=0$ OR whether it should be $y=\frac{3}{4}x+\frac{1}{2}$.
The solutions say $3x-4y+2=0$ should be the answer; however, it doesn't ask for a specific form of the equation. Could it be both?
Actually I'd use neither!
The important parts here are that it passes through a particular point and goes in a particular direction, which means that point-slope form is best:
$$y-2 = \frac{3}{4}(x-2)$$