Question

The eccentricity of the hyperbola `x^2/a^2 - y^2/b^2` = 1 which passes through the points (3, 0) and `(3 sqrt(2), 2)` is ______.

Answer 1

The eccentricity of the hyperbola `x^2/a^2 - y^2/b^2` = 1 which passes through the points (3, 0) and `(3 sqrt(2), 2)` is e² = `13/9`.

Explanation:

Given that the hyperbola `x^2/a^2 - y^2/b^2` = 1 is passing through the points (3, 0) and `(3 sqrt(2), 2)`

So we get a² = 9 and b² = 4

Again, we know that b² = a²(e² – 1).

This gives 4 = 9(e² – 1)

or e² = `13/9`

or e = `sqrt(13)/3`.