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KCET2011MathematicsHyperbola

The equation of a hyperbola whose asymptotes are 3 x 5 y=0 and vertices are ( 5,0) is

Options

  1. A3 x²-5 y²=25
  2. B5 x²-3 y²=225
  3. C25 x²-9 y²=225
  4. D9 x²-25 y²=225

Correct answer

D. 9 x²-25 y²=225

Step-by-step solution

The given equation of asymptotes of hyperbola is array cc 3 x 5 y=0 and vertices & ( 5,0) array Now, equation of hyperbola is gathered (3 x+5 y)(3 x-5 y)= 9 x²-25 y²= gathered Since, ( 5,0) is the vertices of the hyperbola, then 9(5)²-0= =225 From Eq. (ii), 9 x²-25 y²=225

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