You do exactly as you describe, but instead of (2,4) or (3,9), use . So you have one equation representing a whole bunch of lines - it depends on what you choose for .
Now you plug in your point and solve for . That gives you the equation for the line and the point where it's tangent to the parabola.
Not all points will work, by the way. If you try to plug in, say, (1,2), you should find that there's no that works.