Saved Bookmarks
| 1. |
Find the equation of all lines having slope ` 1`that are tangents to the curve `y=1/(x-1), x!=1`. |
|
Answer» Equation of the curve, `y = 1/(x-1)` `:.` Slope of tangent,`( dy/dx) = -1/(x-1)^2` Slope of tangent to this curve is given `-1`. `:. -1/(x-1)^2= -1` `:. x = 0 and x = 2` `=>y = -1 and y = 1` Therefore, equation of tangents to the given curve, `(y+1)/(x-0) = -1 and (y-1)/(x-2) = -1` `=>x+y+1 = 0 and x+y-3 = 0`, which are the required equations. |
|