Question

Which of the following is INCORRECT for the hyperbola $x^2-2y^2-2x+8y-1=0$

• A. Its eccentricity is
• B. Length of the transverse axis is
• C. Length of the conjugate axis is
• D. Latus rectum

Answer 1

The correct option is A

Its eccentricity is

The equation of the hyperbola is $x^2-2y^2-2x+8y-1=0$

$Or(x-1{)}^2-2(y-2{)}^2+6=0$

$Or\frac{(x-1{)}^2}{-6}+\frac{(y-2{)}^2}{3}=1;or\frac{(y-2{)}^2}{3}-\frac{(x-1{)}^2}{6}=1\to 1$

$Or\frac{Y^2}{3}-\frac{X^2}{6}=1;$, where X = x -1 and Y = y -2 $\to$ 2

$\therefore$ the centre=(0,0)in the X-Y coordinates.

$\therefore$ the centre=(1,2)in the x-y coordinates .using $\to$ 2

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 $b^2=a^2(e^2-1)$

$\therefore 6=3(e^2-1),\therefore e^2=3ore=\sqrt{3}$

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

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

Latus rectum $4\sqrt{3}$