The focus of the parabola 4y2+12x−20y+67=0

The given equation of the parabola can be written as  y2−5y=−3x−67/4⇒(y−5/2)2=−3(x+7/2)⇒Y2=4aX where Y=y−5/2,X=x+7/2and a=−3/4The focus of Y2=4aX is (X,Y)=(a,0)=(−3/4,0)⇒x+7/2=−3/4,y−5/2=0⇒x=−17/4,y=5/2Therefore, required focus is (– 17/4, 5/2)