(b) For what value of t the point `(t^2-(2+sqrt3)t+2sqrt3,8)` lie on the y-axis ?

(a) Find the value of t if the point (4,t^2-4t+4) lie on the x-axis.

(vi) Find the value of t if the point (2,t^2-5t-6) lie on the x-axis.

For what values of a^(2) does the point (2sqrt(3), 1) lie outside the ellipse (x^(2))/(a^(2)) +(y^(2))/(4) = 1 ?

Show that for all values of t the point x=c((1+t^2)/(1-t^2)) , y=(2ct)/(1-t^2) lia.on a on a fixed hyperbola. What is the eccentricity of the hyperbola.

From any point P on the parabola y^(2)=4ax , perpebdicular PN is drawn on the meeting it at N. Normal at P meets the axis in G. For what value/values of t, the point N divides SG internally in the ratio 1 : 3, where S is the focus ? a. sqrt((3)/(5)) b. -sqrt((5)/(3)) c. -sqrt((3)/(5)) d. sqrt((5)/(3))

The least distance of the point (2 sin t, 2 cos t, 3 t) from the origin is

Show that for all values of t the point x = a. (1 + t^(2))/(1-t^(2)), y = (2at)/(1-t^(2)) lies on a fixed hyperbola. What is the value of the eccentricity of the hyperbola?

The least distance of the point ( 2 soin t , 2 cos t , 3t) from the origin is _