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Question

Which of the following is INCORRECT for the hyperbola x22y22x+8y1=0



Correct Answer
A

Its eccentricity is

Your Answer
B

Length of the transverse axis is

Your Answer
C

Length of the conjugate axis is

Your Answer
D

Latus rectum


Solution

The correct option is A

Its eccentricity is


The equation of the hyperbola is  x22y22x+8y1=0

Or (x1)22(y2)2+6=0

Or (x1)26+(y2)23=1 ; or (y2)23(x1)26=11

Or Y23X26=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(e21)

6=3(e21),e2=3 or e=3

The length of the transverse axis = 23

The length of the conjugate axis =  26

Latus rectum 43

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