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Question

The vertices of a hyperbola are at (0,0) and (10,0) and one of its foci is at (18,0). The equation of the hyperbola is

A
x225y2144=1
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B
(x5)225y2144=1
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C
x225(y5)2144=1
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D
(x5)225(y5)2144=1
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Solution

The correct option is B (x5)225y2144=1
Distance between vertices is =2a=100=10a=5
Distance between vertex and focus =aea=8
e=1+85=135
b=5×(13)2521=5×125=12
Centre of hyperbola (midpoint of the line joining the two foci) =(5,0)
(x5)225y2144=1

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