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Question

The vertices of the hyperbola 9x216y236x+96y252=0 are

A
and
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B
and
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C
and
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D
None of these
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Solution

The correct option is B and
We have, 9(x24x+4)16(y26y+9)=144
(x2)242(y3)232=1
Shifting the origin at (2, 3), we have x242y232=1 Where, x = X + 2, y = Y + 3. Then coordinates of the vertices are x=±4,Y=3 i.e. x=6,y=3 and x=2,y=3

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