Question

The line l is tangent to the circle with equation x2 + y2 = 17 at the point P.
Determine the equation of line l.

Answer 1

The line is perpendicular to the line from origin to P (by tangent is perpendicular to radii)
Which slope is 1/4
So the
(slope of tangent) x (1/4) = -1

Slope of tangent = -4
Point slope form:
(y-1)/(x-4)=-4
y-1=-4x+16
y=-4x+17


Or you can construct the upper half of the circle in y=(17-x^2)^(1/2) and differentiate it to get the slope then use point slope form again