Question

The length of the conjugate axis of the hyperbola $9x^2-90x-25y^2+150y-225=0$ is units

Answer 1

Given equation is $9x^2-90x-25y^2+150y-225=0$
$\Rightarrow 9(x^2-10x+25)-25(y^2-6y+9)=225$
$\Rightarrow \frac{(x-5{)}^2}{25}-\frac{(y-3{)}^2}{9}=1$
Here $b^2=9\Rightarrow b=3$
Length of conjugate axis $=2b=6$ units