The tangent line is perpendicular to this radius, so we have to figure out what
the equation for the radius is at this point. We know the center is (0,0), and the
point is (4,3). We can use the point-slope formula to derive the slope of the line
through those two points. For any two points (x 1 , y 1 ) and (x 2 , y 2 ), we can say
So:So now we know that the slope of this radius is ¾. We’re trying to get the
equation of the tangent line, so we need the perpendicular slope, which is –^4 / 3.
Now all we have to do is plug everything into an equation:And we have our tangent line.
Note that this also could have been written as