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

The angle between the curves x²=4y, x²+y²=5 at (-2, 1) is

The equation of the tangent to the curve x²+2y=8 and which is perpendicular to x-2y+1=0 is

The condition for f(x)= x³+px²+qx+r(x R) to have no extreme value, is

When a circular oil drop expands on water, its area increases at the uniform rate of 40sq. cm per minute. The rate of increase in the radius when the radius 5 cm is