a) Koordinati točke $A(-\sqrt 5 , 2\sqrt 3)$ vstavimo v enačbo hiperbole $6x^2-5y^2+30=0$.

$ 6\cdot (-\sqrt 5)^2-5\cdot(2\sqrt 3)^2+30=0$

$6\cdot 5-5\cdot 12+30=0$

$0=0$

Točka $A$ leži na hiperboli.

b) Ordinato točke $B(x,3)$ vstavimo v enačbo hiperbole $6x^2-5y^2+30=0$.

$6x^2-5\cdot 3^2+30=0$

$6x^2=15$

$\displaystyle x^2=\frac{15}{6}$

$\displaystyle x=\pm\frac{\sqrt{10}}{2} $

$\displaystyle B_1\left( \frac{\sqrt{10}}{2},3\right),\; B_2\left( -\frac{\sqrt{10}}{2},3\right)$

Elipsa:

$5x^2+9y^2=45$

$\displaystyle\frac{x^2}{9}+\frac{y^2}{5}=1$ 

$a=3,\; b=\sqrt 5$

$e^2=a^2-b^2\Rightarrow e=2$

Hiperbola:

$a=2,\; e=3$

$b^2=e^2-a^2\Rightarrow b=\sqrt 5$

$\displaystyle\frac{x^2}{4}-\frac{y^2}{5}=1$