Answer to Question #2062 in Calculus for vinay

Question

Find the angle between the y-axis and the tangent to the hyperbola xy =1 at (1, 1).

Answer 1

The equation of the tangent to y(x) = 1/x at (1,1) is
y-1 =
<img src="/cgi-bin/mimetex.cgi?y-1%20=%20y%27%281%29%28x-1%29%5C%5C%20y-1%20=%20-%5Cfrac%7B1%7D%7B1%5E2%7D%28x-1%29%20=%201%20-x%20%5C%5C%20y%20=%20-x%20%5C%5C" title="y-1 = y'(1)(x-1)\\ y-1 = -\frac{1}{1^2}(x-1) = 1 -x \\ y = -x \\">
The angle between the positive direction of the y-axis is 180-45 = 135 degrees.