Here foci are (0, ± $\sqrt{10}$) which lie on y-axis. So the equation of hyperbola in standard form is $\frac{y^2}{a^2} - \frac{x^2}{b^2}$ = 1 Now, foci are (0, ± $\sqrt{10}$) ⇒ c = $\sqrt{10}$ We know that $c^2$ = $a^2 + b^2$ ⇒ $(\sqrt{10})^2$ = $a^2+b^2$ ⇒ $b^2$ = 10 - $a^2$ Since the hyperbola passes through (2, 3) ∴ $\frac{9}{a^2} - \frac{4}{b^2}$ = 1 ⇒ $\frac{9}{a^2} - \frac{4}{10-a^2}$ = 1 ⇒ 9(10 − $a^2$) − $4a^2$ − $a^2(10 - a^2)$ = 0 ⇒ $a^4 - 23a^2$ + 90 = 0 ⇒ $a^4 - 18a^2 - 5a^2$ + 90 = 0 ⇒ ($a^2$ – 18)($a^2$ – 5) = 0 ⇒ $a^2$ = 18 or $a^2$ = 5 When $a^2$ = 18 then $b^2$ = 10 – 18 = –8 (which is not possible) When $a^2$ = 5, then $b^2$ = 10 – 5 = 5 Thus, required equation of hyperbola is $\frac{y^2}{5} - \frac{x^2}{5}$ = 1.