Which of the following equations in parametric form can represent a hyperbolic profile , where `t` is a parameter : `(A)x=a/2(t+1/t) & y=b/2(t-1/t)` `(B)tx/a-y/b+t=0 & x/a+ty/b-1=0` `(C)x=e^t+e^(-t) & y=e^t-e^(-t)` `(D)x^2-6=2cost & y^2+2=4cos^(t/2)`

Which of the following equations in parametric form can represent a hyperbolic profile, where t is a parameter: (A)x=(a)/(2)(t+(1)/(t))&y=(b)/(2)(t-(1)/(t))(B)t(x)/(a)-(y)/(b)+t=0&(x)/(a)+t(y)/(b)-1=0(C)x=e^(t)+e^(-t)&y=e^(t)-e^(-t)(D)x^(2)-6=2cos t&y^(2)+2=4cos^((t)/(2))

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

If t is a parameter and x = t + 1/t , y = t - 1/t , " then " (d^2 y)/(dx^2) =

If t is a parameter and x = t + 1/t , y = t - 1/t , " then " (d^2 y)/(dx^2) =

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

If t is a variable parameter, show that x=(a)/(2)(t+(1)/(t)) and y = (b)/(2)(t-(1)/(t)) represent a hyperbola.