If the curves `y=ax^(3)-3ax+4a` and `y=12x+4a` touches at `x=0` then `a`=

Prove that the curves y=x^(3)-3x^(2)-8x-4,y=3x^(2)+7x+4 touch each other and equation of the common tangent is x-y+1=0 .

(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"

If the line y=4x+2 touches the curve y=a+bx+3x^(2) at the point where it crosses the Y-axes , then : (a,b)-=

If the curve y=ax^(3) +bx^(2) +c x is inclined at 45^(@) to x-axis at (0, 0) but touches x-axis at (1, 0) , then

Equations of tangents to the curve y=2x^(3)-3x^(2)-12x+20 , which are parallel to the X-axes, are

The curve y = ax ^(3) + bx ^(2) + cx + 5 touches the x-axis at P (-2, 0) and cuts the y-axis at a point Q where its gradient is 3, then 2a + 4b is equal to :

If the curves 2x^(2)+3y^(2)=6 and ax^(2)+4y^(2)=4 intersect orthogonally, then a =

If the line ax + y = c , touches both the curves x^(2) + y^(2) =1 and y^(2) = 4 sqrt2x , then |c| is equal to:

If the circle x^(2)+y^(2)+2ax=0, a in R touches the parabola y^(2)=4x , them