Question

The length of the intercept on y-axis cut off by the parabola, $y^2-5y=3x-6$ is ?

Answer 1

$y^2-5y=3x-6$
For point of intersection with $Y-$ axis i.e. $X=0$
$y^2-5y=3\times 0-6$
$y^2-5y+6=0$
$(y-2)(y-3)=0$
$y=2,3$
$A(0,y_1)B(0,y_2)$
$\therefore AB=|y_1-y_2|=|3-2|=1$