Find the locus of the point `(t^2-t+1,t^2+t+1),t in Rdot`

Find the angle at which normal at point P(a t^2,2a t) to the parabola meets the parabola again at point Qdot

Let z=t^2-1+sqrt(t^4-t^2),w h e r et in R is a parameter. Find the locus of z depending upon t , and draw the lous of z in the Argand plane.

If int_0^1(e^t)/(1+t)dt=a , then find the value of int_0^1(e^t)/((1+t)^2)dt in terms of a .

Find the derivatives of the following : x = (1-t^2)/(1+t^2), y = (2t)/(1+t^2)

Find Distance between the points for which lines that pass through the point (1, 1) and are tangent to the curve represent parametrically as x = 2t-t^2 and y = t + t^2

Find the points of minima for f(x)=int_0^x t(t-1)(t-2)dt

Find the coefficient of t^8 in the expansion of (1+2t^2-t^3)^9 .