If the normal to the curve x³-y² =0 at (m², -m³) is y=mx-2m³, then the value of m²  is

The curves y=x²-1, y=8x-x²-9 touch each other at the point (2, 3). The equation of the common normal is

If the subnormal of the curve xyⁿ=aⁿ⁺¹ is constant, then the value of n is

The equation of tangent to the curve y=x+9/x+5 so that is passes through the origin is

If θ is the angle between the curves y=sin x, y =cosx at x=π/4 then tan θ=

A curve passes through the point (2, 0) and the slope of the tangent at any point is x²-2x for all values of x. The point of maximum or donation the curve is

The function f(x) = tan x has

f(x)= x-1/x is

The function f(x)=cot^-1 x+x increases in the interval

The point P in the first quadrant of the ellipse x²/8+y²/18=1 so that the area of the triangle formed by the tangent at P and the coordinate axes is least