Mathematics - Hyperbola Question with Solution | TestHub

The equation of the hyperbola is

Or

Or

or

Or

, where X = x -1 and

∴ the centre=(0,0)in the X-Y coordinates.

∴ the centre=(1,2)in the x-y coordinates .using

If the transverse axis be of length 2a, then a= $\sqrt{3}$

,since in the equation (1) the transverse axis is

parallel to the y-axis. If the conjugate axis is of length 2b,then b = $\sqrt{6}$

But

∴ 6= 3 (e²-1), ∴ e² = 3 or

The length of the transverse axis =$2\sqrt{3}$

The length of the conjugate axis = $2\sqrt{6}$