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

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

Assertion (A): The locus of the point ((e^(2t)+e^(-2t))/(2), (e^(2t)-e^(-2t))/(2)) when 't' is a parameter represents a rectangular hyperbola. Reason (R ) : The eccentricity of a rectangular hyperbola is 2.

Assertion (A): The locus of the point ((e^(2t)+e^(-2t))/(2), (e^(2t)-e^(-2t))/(2)) when 't' is a parameter represents a rectangular hyperbola. Reason (R ) : The eccentricity of a rectangular hyperbola is 2.

The normal at P to a hyperbola of eccentricity e, intersects its transverse and conjugate axes at L and M respectively.Show that the locus of the middle point of LM is a hyperbola of eccentricity (e)/(sqrt(e^(2)-1))

The normal at P to a hyperbola of eccentricity e , intersects its transverse and conjugate axes at L and M respectively. Show that the locus of the middle point of LM is a hyperbola of eccentricity e/sqrt(e^2-1)

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

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