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`

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 bouyped by the hyperbola and the lines joining its centre to the points corresponding to t_(1)and-t_(1) ist _(1) .

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

The equations x=(e^t+e^(-t))/2,y=(e^(t)-e^(-t))/2, t inR represent :

Show that the tangents and the normals to the parabola x=at^(2),y=2at at points corresponding to t=1 and t=-1 form a square.

If x=(e^(t)+e^(-t))/(2),y=(e^(t)-e^(-t))/(2)," then: "(dy)/(dx)=

If x=(e^(t)+e^(-t))/(2),y=(e^(t)-e^(-t))/(2)," then: "(dy)/(dx)=

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

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