The values of ‘a’ for which the function (a+2)x³-3ax²+9ax-1 decreases monotically throughout for all real x are

The equation of the normal to the curve x²=4y at (2, 1) is

Equation of the tangent to the curve  y=2x³+6x²-9 at the point where  the crosses the y-axis curve is

The angle between the curves y²=4ax, ay= 2x² is

If θ is the angle between the curves xy=2, x² +4y=0 then tan θ=

For the curve y²=(x+a)³, the square of the sub tangent is……. Subnormal

If f(x)=x-k/x has a maximum value at x=-2. Then k=

The length of the sub tangent to the curve x²y²=a⁴ at the point (-a, a) is

The two curves y=x^-3, y=e^3(1-x) at (1, 1)

The distance between the origin and the normal to the curve y=e^2x+x² at x=0 is