Discuss monotonocity of `y=f(x)` which is griven by `x=1/(1+t^2)a n dy=1/(t(1+t^2))`

A function y=f(x) is given by x=1/(1+t^2) and y=1/(t(1+t^2)) for all tgt0 then f is

Find (dy)/(dx) , when x=(1-t^2)/(1+t^2) and y=(2t)/(1+t^2)

Find (dy)/(dx) , when x=(2t)/(1+t^2) and y=(1-t^2)/(1+t^2)

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.

Find (dy)/(dx), when x=(3a t)/(1+t^2)" and "y =(3a t^2)/(1+t^2)

The eccentricity of the conic x=3((1-t^(2))/(1+t^(2))) and y=(2t)/(1+t^(2)) is

The locus represented by x=a/2(t+1/t), y=a/2(t-1/t) is

Find the eccentricity of the hyperbola given by equations x=(e^t+e^(-1))/2a n dy=(e^t-e^(-1))/3,t in Rdot

If sinx=(2t)/(1+t^2),tany=(2t)/(1-t^2),"f i n d"(dy)/(dx)dot