10.5 The Hyperbola

Foci are on y-axis, so equation is $\frac{y^2}{a^2} - \frac{x^2}{b^2} = 1$. Given $c = 3$ and $a = \frac{\sqrt{11}}{2}$. Relation: $c^2 = a^2 + b^2$. $9 = \frac{11}{4} + b^2$ $b^2 = 9 - 2.75 = 6.25 = \frac{25}{4}$. Equation: $\frac{y^2}{11/4} - \frac{x^2}{25/4} = 1$ $4y^2/11 - 4x^2/25 = 1 \implies 100y^2 - 44x^2 = 275$