The length of the tangent of the curves x=a cos ³θ, y= a sin³θ (a>0) is

The point of the curve y=x⁴-4x³+4x²+1 at which the tangent is parallel to x-axis is

Tangent at any point of the curve (x/a)^2/3+(y/b)^2/3=1 makes intercepts x₁and y₁ on the axes. Then

The area of the triangle formed by the tangent to the curve y=8/(4+x²) at x=2 and the co-ordinate axes is

The angle between the curve y²=4x+4 and y²=36(9-x) is

The length of the normal of the curve 2x²+3xy-2y²=8 at (2, 3) is

If θ is the angle of intersection of the curves y²=x³ and y=2x²-1 at (1, 1), then tanθ=

If θ is the angle between the curves xy=2, y² =4x at (1, 2) then tan θ=

At a given instant the legs of a right angled triangle are 8 inch and 6 inch respectively. The first leg decreases at 1 inch per minute and second increases at 2 inch per minute. The rate of increasing of the area after 2 minutes is

If an error of 0.01 cm is made while measuring the radius 5 cm of a circle, then the relative error in the area is