Question

# Which of the following is INCORRECT for the hyperbola x2−2y2−2x+8y−1=0

A

Its eccentricity is

B

Length of the transverse axis is

C

Length of the conjugate axis is

D

Latus rectum

Solution

## The correct option is A Its eccentricity is The equation of the hyperbola is  x2−2y2−2x+8y−1=0 Or (x−1)2−2(y−2)2+6=0 Or (x−1)2−6+(y−2)23=1 ; or (y−2)23−(x−1)26=1→1 Or Y23−X26=1;, where X = x -1 and Y = y -2 → 2 ∴ the centre=(0,0)in the X-Y coordinates. ∴ the centre=(1,2)in the x-y coordinates .using  → 2 If the transverse axis be of length 2a, then a = √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 = √6 But b2=a2(e2−1) ∴6=3(e2−1),∴e2=3 or e=√3 The length of the transverse axis = 2√3 The length of the conjugate axis =  2√6 Latus rectum 4√3

Suggest corrections