Question

The equation of a hyperbola is given by \(\frac{{{x^2}}}{9} - \frac{{{y^2}}}{{25}} = 1\). The eccentricity of the hyperbola will be 
1. \(\frac{\sqrt {34}}{3}\)
2. √34 
3. √17 
4. \(\frac{\sqrt {17}}{3}\)

Answer 1

Correct Answer - Option 1 : \(\frac{\sqrt {34}}{3}\)

Concept:

The general equation of hyperbola is given by

\(\frac{{{{(x - h)}^2}}}{{{a^2}}} - \frac{{{{\left( {y - k} \right)}^2}}}{{{b^2}}} = 1\)

The eccentricity is given by

\(e = \frac{{\sqrt {{a^2} + {b^2}} }}{a}\)

 

Calculation:

Given hyperbola is \(\frac{{{x^2}}}{9} - \frac{{{y^2}}}{{25}} = 1\);

Comparing with general equation, a = 3, b =5;

Now the eccentricity will be

\(e = \frac{{\sqrt {{3^2} + {5^2}} }}{3} = \frac{\sqrt{34}}{3}\)