Correct Answer – Option 1 : 9x² – 25y² = 225

Concept:

The equation of the hyperbola is:

\(\frac{{{x^2}}}{{{a^2}}} – \frac{{{y^2}}}{{{b^2}}} = 1\) 

The vertices are (± a, 0)

The asymptotes are the straight lines:

y = (b/a)x and y = -(b/a)x.

Given:

Vertices are (± 5, 0)       

Asymptotes are: 3x ± 5y = 0

Analysis:

5y = 3x & 5y = -3x

\(y = \left( {\frac{3}{5}} \right)x\;\& \;y = – \left( {\frac{3}{5}} \right)x\) 

∴ a = 5 and b = 3

Equation of hyperbola:

\(\frac{{{x^2}}}{{25}} – \frac{{{y^2}}}{9} = 1\) 

9x² – 25y² = 225