Question

Find the vertex, axis, focus, and latus rectum of the parabola
$4y^2+12x-20y+67=0$

Answer 1

$4y^2+12x-20y+67=0$

$4y^2-20y=-12x-67$

$(y-\frac{5}{2}{)}^2=-3(x-\left(\frac{-7}{2}\right))$

$\therefore$ Vector is $(\frac{-7}{2},\frac{5}{2})$

$a=\frac{3}{4}$

Focus $(h-a,k)$

$(\frac{-7}{2}-\frac{3}{4},\frac{5}{2})$

Focus $(\frac{-17}{4},\frac{5}{2})$

equation of axis $y=\frac{5}{2}$

equation of directeri $xx=\frac{3}{4}$

$(\because x=a)$

Latus rectum $4a=3$