For the hyperbola 9x2−16y2−18x+32y−151=0

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one of the directrix is x=21/5

the length of latus rectum is 92

foci are (6, 1) and (-4,1)

the eccentricity is 5/4

answer is A.

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Detailed Solution

The given hyperbola can be written as(x−1)216−(y−1)29=1or X216−Y29=1 (where X=x−1,Y=y−1 ) e=1+b2a2=1+916=54Directrices areX=±a/e. Therefore, x−1=±165or x=215 and x=−115Length of latus rectum =2b2a=92The foci are given byX=±ae,Y=0 or (6,1),(−4,1)

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