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If the product of the perpendicular distances from any point on the hyperbola  of eccentricity e= on its asymptotes is equal to 6, then the length of the transverse axis of the hyperbola is
  • a)
    3
  • b)
    6
  • c)
    8
  • d)
    12
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
If the product of the perpendicular distances from any point on the hy...
e2 = (a/ b2) + 1
3 = (a2 / b2) + 1
a2/b2 = 2
a2 = 2b2
Product of perpendicular distance of any point on hyperbola = (a2b2)/a2 + b2
= [2(b2).b2]/(2b2 + b2)
= [2b2]/3 = 6
= 2b2 = 18
=> b2 = 9
=> b = 3
Length (2b) = 2(3) 
= 6
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If the product of the perpendicular distances from any point on the hy...
e2 = (a/ b2) + 1
3 = (a2 / b2) + 1
a2/b2 = 2
a2 = 2b2
Product of perpendicular distance of any point on hyperbola = (a2b2)/a2 + b2
= [2(b2).b2]/(2b2 + b2)
= [2b2]/3 = 6
= 2b2 = 18
=> b2 = 9
=> b = 3
Length (2b) = 2(3) 
= 6
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If the product of the perpendicular distances from any point on the hyperbolaof eccentricity e= on its asymptotes is equal to 6, then the length of the transverse axis of the hyperbola isa)3b)6c)8d)12Correct answer is option 'B'. Can you explain this answer?
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