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`

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

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

If ''e' denotes the eccentricity of the hyperbola, satisfying the differential equation 2xy(dy)/(dy)=x^(2)+y^(2) and passing through the point (2,1),then(e^(2)-1) is equal to

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

If e and e_(1) , are the eccentricities of the hyperbolas xy=c^(2) and x^(2)-y^(2)=c^(2) , then e^(2)+e_(1)^(2) is equal to