Prove that the point `{(a)/(2)(t+(1)/(t)), (b)/(2)(t-(1)/(t))}` lies on the hyperbola for all values of `t(tne0)`.

Show that the locus represented by x=(1)/(2)a(t+(1)/(t)),y=(1)/(2)a(t-(1)/(t)) is a rectangular hyperbola.

Show that the locus represented by x=(1)/(2)a(t+(1)/(t)),y=(1)/(2)a(t-(1)/(t)) is a rectangular hyperbola.

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.

The locus of the point ( (e^(t) +e^(-t))/( 2),(e^t-e^(-t))/(2)) is a hyperbola of eccentricity

The locus of a point represent by x=(a)/(2)((t+1)/(t)),y=(a)/(2)((t-1)/(t)) , where t=in R-{0} , is

Prove that t^(2) + 3t + 3 is a factor of ( t+1)^(n+1) + (t+2)^(2n -1) for all intergral values of n in N.

For any real t ,x=1/2(e^t+e^(-t)),y=1/2(e^t-e^(-t)) is a point on the hyperbola x^2-y^2=1 Show that the area bounded by the hyperbola and the lines joining its centre to the points corresponding to t_1a n d-t_1 is t_1dot

Find the value of ln(int_(0)^(1) e^(t^(2)+t)(2t^(2)+t+1)dt)

If the points (0,0), (1,0), (0,1) and (t, t) are concyclic, then t is equal to