The equation of the tangent to the curve  (x/a)^2/3+(y/b)^2/3 =1 at (a cos³θ, b sin³θ ) is

If A, B, C, D are the length of tangents to the curves 1.y=4x² at (-1, 4) 2. Y=x³+1 at (1, 2) 3. Y=x³/2-x at (1, 1) 4. 2x²+3xy-2y²=8 at (2, 3) then the ascending order of A, B, C, D is

The distance from a fixed point O of a particle P moving in a straight line from O is given by s=16+48t-t³. The direction of motion of the particle after t=4 sec is

The point on the curve y=x²+5, the tangent at which  is perpendicular to the line x+2y=2 is

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