Question

Write an equation for the line tangent to the circle x2 + y2 = 17, at the point (4, 1). Enter your answer in point-slope form: y - y1 = m(x - x1)

Answer 1

The slope of a line at a given point is equal to its derivative at that point:
2xdx + 2ydy = 0
-2ydy = 2xdx
dy/dx = -x/y
Slope = -(4/1)
= -4

Equation:
y - 1 = -4(x - 4)