Correct Answer - Option 1 : 9x
2 - 25y
2 = 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