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Question

Equation of one of the tangents passing through (2,8) to the hyperbola 5x2y2=5 is

A
3xy2=0
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B
23x3y22=0
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C
x+y+3=0
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D
10x8y5=0
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Solution

The correct option is B 23x3y22=0
Equation of the hyperbola is 5x2y2=5x21y25=1
Here, a2=1 and b2=5
Equation of the tangent is y=mx±a2m2b2 and it passes through (2,8)
8=2m±m25
(82m)2=m25
64+4m232m=m25
3m232m+69=0
3m29m23m+69=0
(3m23)(m3)=0
m=233,3
Therefore, equation of required tangent's are
y=3x+2 and 23x3y22=0

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