JEE Advance - Mathematics (1982 - No. 3)
For any real $$t,\,x = {{{e^t} + {e^{ - t}}} \over 2},\,\,y = {{{e^t} - {e^{ - t}}} \over 2}$$ is a point on the
hyperbola $${x^2} - {y^2} = 1$$. Show that the area bounded by this hyperbola and the lines joining its centre to the points corresponding to $${t_1}$$ and $$-{t_1}$$ is $${t_1}$$.
hyperbola $${x^2} - {y^2} = 1$$. Show that the area bounded by this hyperbola and the lines joining its centre to the points corresponding to $${t_1}$$ and $$-{t_1}$$ is $${t_1}$$.
The area bounded by the hyperbola and the lines joining its center to the points corresponding to t1 and -t1 is indeed t1.
The parametric equations given describe a circle, not a hyperbola.
The area described can be calculated using integration and hyperbolic functions.
The given parametric equations satisfy the equation x^2 - y^2 = 1.
The area is 2*t1
Comments (0)
