The point on the curve x²=2y which is closest to the point (0, 5) is

The approximate change in y, when y=x²+2x, x=3, δx=0.01 is

If the tangent to the curve xy+ax+by=0 at (1, 1) is inclined at an angle tan^-2 with x-axis, then

The angle between the curves x²+y²=4 and x²=3y is

Equation of the tangent line at y=a/4 to the curve y(x²+a²)=ax² is

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