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Question

If the eccentricity and length of latus rectum of a hyperbola are 133 and 103 units respectively, then what is the length of the traverse axis?

A
72 units
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B
12 units
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C
152 units
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D
154 units
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Solution

The correct option is C 152 units
formulaused
L=2b2a
e=1b2a2
Lengthoftransverseaxis=2a
Given
e=133,L=103
2b2a=103
b2=5a3
b2=a2(e21)
5a3=a2(1391)
5a3=a2(49)
4a215a=0
a(4a15)=0
a=0,154
a0
Hencea=154
Lengthoftransverseaxis=2a
=154(2)
=152

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