Show that the point (x,y) given y `x = ( 2at)/( 1+t^(2))` and `y = (a( 1-t^(2)))/( 1+t^(2))` lies on a circle..

Show that the point (x,y) given by x = (2at)/(1 + t^(2)) and y = (a(1-t^(2)))/(1+t^(2)) lies on a circle for all real values of t such that -1 lt t lt 1 where a is any given real numbers.

Show that the point (x,y) given by x=(2at)/(1+t^(2)) and y=((1-t^(2))/(1+t^(2))) lies on a circle for all real values of t such that -1<=t<=1 where a is any given real number.

Show that the point (x ,y) given by x=(2a t)/(1+t^2)a n dy=((1-t^2)/(1+t^2)) lies on a circle for all real values of t such that -1lt=tlt=1, where a is any given real number.

Show that the point (x ,y) given by x=(2a t)/(1+t^2)a n dy=((1-t^2)/(1+t^2)) lies on a circle for all real values of t such that -1lt=tlt=1, where a is any given real number.

Show that the point : x=(2rt)/(1+t^2), y=(r(1-t^2))/(1+t^2) (r constant) lies on a circle for all values of t such that -1 le t le 1 .

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?

If x = (2at)/(1 + t^2) , y = (a(1-t^2) )/(1 + t^2) , where t is a parameter, then a is

If t be a variable parameter, show that the point x = a(1 -t^(2))/(1+t^(2)),y = b(2t)/(1 + t^(2)) always lies on an ellipse .

A function y=f(x) is given by x=(1)/(1+t^(2)) and y=(1)/(t(1+t^(2))) for all t>0 then f is