The tangent at 't' of the curve `y = 8t^3 -1, x = 4t^2 +3` meets the curve at `t_1` and is normal to the curve at `t_1.` Then the value of t is

The tangent at (t,t^(2)-t^(3)) on the curve y=x^(2)-x^(3) meets the curve again at Q, then abscissa of Q must be

If the tangent to the curve x = t^(2) - 1, y = t^(2) - t is parallel to x-axis , then

If the tangent drawn at P(t=(pi)/(4)) to the curve x=sec^(2)t, y=cot t meets the curve again at R ,then PR=

The slope of the tangent to the curve x=at^3,y=at^4 at t=1 is

The slope of the tangent to the curve x = t^2+3t-8, y = 2t^2-2t-5 at the point (2,-1) is:

If the tangent at a point P with parameter t , on the curve x=4t^2+3 , y=8t^3-1 t in R meets the curve again at a point Q, then the coordinates of Q are