" (iii) "3sqrt(t)+t sqrt(2)

The eccentricity of the hyperbola x=a/2(t+1/t), y=a/2(t-1/t) is a. sqrt(2) . b. sqrt(3) c. 2sqrt(3) d. 3sqrt(2)

Differentiate w.r.t. time. (i) y=t^(2) " " (ii) x=t^(3//2)" " (iii) y=(1)/(sqrt(t)) (iv) x=4t^(3) " " (v) y=2sqrt(t) " " (vi) y=2t^(2)+t-1 (vii) y=3sqrt(t)+(2)/(sqrt(t)) (viii) y=t^(3)sin t " " (ix) x=te^(t) (x) x= sqrt(t)(1-t)

Find (dx)/(dt) when x = sin^-1(t.sqrt(1-t) +sqrt(t) sqrt(1-t^2)) .

The length of latusrectum of the parabola whose parametric equations are x=t^2+t+1,y=t^2-t+1, where t in R is equal to (1) sqrt(2) (2) sqrt(4) (3) sqrt(8) (4) sqrt(6)

The length of latusrectum of the parabola whose parametric equations are x=t^2+t+1,y=t^2-t+1, where t in R is equal to (1) sqrt(2) (2) sqrt(4) (3) sqrt(8) (4) sqrt(6)

If x = sqrt((1 - t^2)/(1 + t^2)), y = (sqrt(1 + t^2) - sqrt(1 - t^2))/(sqrt(1 + t^2) + sqrt(1 -t^2)) then (dy)/(dx) =