Find the vertex, focus, axis , latus rectum and directrix of the parab

1.	Find the vertex, focus, axis , latus rectum and directrix of the parabola `y^(2)+4x+6y+17=0`
Answer» Equation of parabola `y^(2)+4x+6y+17=0` `rArr" "y^(2)+6y+9=-4x-17+9` `rArr" "(y+3)^(2)=-4(x+2)` `rArr" "Y^(2)=-4X` Comparing with `Y^(2)=-4aX` 4a=4 `rArr" "a=1` Vertex A = (0,0) `rArr" "X=0,Y=0` `rArr" "x+2=0,y+3=0` `rArr" "x=-2,y=-3` `:.` Co-ordinates of vertex = (-2,-3). Focus X = -a,Y=0 `rArr" "x+2=-1,y+3=0` `rArr" "x=-3,y=-3` `:.` Co-ordinates of focus = (-3, -3). Equation of axis Y=0 `rArr" "y+3=0`. Equation of directrix X=a `rArr" "x+2=1` `rArr" "x+1=0` Length of latus rectum = 4a = 4.

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