Question

Write the eccentricity of the hyperbola 9x² − 16y² = 144.

Answer 1

Equation of the hyperbola: \[9 x^2 - 16 y^2 = 144\]                ..... (1)

Equation (1) can be rewritten in the following way:

\[\frac{9 x^2}{144} - \frac{16 y^2}{144} = \frac{144}{144}\]

\[ \Rightarrow \frac{x^2}{16} - \frac{y^2}{9} = 1\]

\[\Rightarrow \frac{x^2}{4^2} - \frac{y^2}{3^2} = 1\]

This becomes the standard equation of the hyperbola with its major axis \[a = 4\] and minor axis \[b = 3\].

Eccentricity, \[e = \frac{\sqrt{a^2 + b^2}}{a}\]

Substituting the value of a and b, we get:

\[e = \frac{\sqrt{4^2 + 3^2}}{4}\]

\[ = \frac{\sqrt{16 + 9}}{4}\]

\[ = \frac{5}{4}\]

Therefore, the eccentricity is \[\frac{5}{4}\].