If the eccentricity of a hyperbola x^29-y^2b^2=1, which passes through (k,2), is √133, the…

Question

If the eccentricity of a hyperbola $\dfrac{x^2}{9}-\dfrac{y^2}{b^2}=1$, which passes through $(k,2)$, is $\dfrac{\sqrt{13}}{3}$, then the value of $k^2$ is:

Accepted Answer

$e^2=1+\dfrac{b^2}{9}=\dfrac{13}{9}\Rightarrow b^2=4$.

Since the hyperbola passes through $(k,2)$: $\dfrac{k^2}{9}-\dfrac{4}{4}=1\Rightarrow\dfrac{k^2}{9}=2\Rightarrow k^2=18.$

Solutions · 1