The hyperbola x2a2−y2b2=1(a,b>0) passes through the point of intersection of the lines 7x+13y−87=0 & 5x−8y+7=0 and the latus rectum is 32√25. The values of a and b are:
A
a=5√2,b=3.
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B
a=5√2,b=4.
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C
a=7√2,b=3.
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D
None of these
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Solution
The correct option is Ba=5√2,b=4. Point of intersection of lines 7x+13y−87=0 & 5x−8y+7=0 is (5,4). Also this point lies on the given hyperbola ∴25a2−16b2=1 ......(1) Also latus rectum LR=2b2a=32√25 ⇒b2=16√2a5 .....(ii) From (i) & (ii) a2=252,b2=16.