If the tangent to the curve `x y+a x+b y=0` at `(1,1)` is inclined at an angle `tan^(-1)2` with x-axis, then find `aa n db ?`

(i) If the tangent to the curve xy+ax+by=0 at (1,1) is inclined at an angle tan^(-1) 2 with positive x-axis in anticlockwise then find a and b? (ii) The curve y=ax^(3) +bx^(2)+3x+5" touches "y=(x+2)^(2) " at "(-2,0) " then "|(a)/(2)+b|" is"

Find tangent of curve y=x^(3)-x at x=1

Find the points on the curve x y+4=0 at which the tangents are inclined at an angle of 45o with the x-axis.

Find the equation of the tangent to the circle x^(2)+y^(2)=25 which is inclined at 60^(@) angle with x -axis

Find the equation of the tangent of the curve y=3x^(2) at (1, 1).

If the tangent to the curve y=x^3+a x+b at (1,\ -6) is parallel to the line x-y+5=0 , find a and b .