Equation of the hyperbola with centre at origin, transverse axis Y-axis and passing through points (4, 6) and (-1, 3) is

Since transverse axis is Y-axis, hyperbola
$\mathrm{H}\equiv \frac{y^2}{a^2}-\frac{x^2}{b^2}=1$ passes through (4, 6) and 
$(-1,3)\Rightarrow \frac{36}{a^2}-\frac{16}{b^2}=1,\frac{9}{a^2}-\frac{1}{b^2}=1$|
solving we get $b^2=4,a^2=\frac{36}{5}$
$\therefore \text{ Equation is }9x^2-5y^2=-36$