Question

The hyperbola $\frac{x^2}{9}-\frac{y^2}{b^2}=1$ passes through the point $(4,5)$ Find 'b'.

Answer 1

The equation of hyperbola is $\frac{x^2}{9}-\frac{y^2}{b^2}=1$

The point is $(4,5)$

$⟹\frac{4^2}{9}-\frac{5^2}{b^2}=1\frac{16}{9}-1=\frac{25}{b^2}\frac{7}{9}=\frac{25}{b^2}{b}^2=\frac{25\times 9}{7}b=\frac{15}{\sqrt{7}}$