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The locus of the point ( (e^(t) +e^(-t))...

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

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The locus of point ((e^(t)+e^(-t))/(2),(e^(t)-e^(-t))/(2)) is a hyperbola with 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 equation x = (e ^(t) + e ^(-t))/(2), y = (e ^(t) -e^(-t))/(2), t in R, represents

The equation x = (e ^(t) + e ^(-t))/(2), y = (e ^(t) -e^(-t))/(2), t in R, represents

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