HURRY! Find the focus, vertex, length of the latus rectum and equation of the directrix for the parabola x2 +2y -3x +5 =0.

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Please find below the solution to the asked query:

We have:x2+2y-3x+5=0x2-3x+5+2y=0x-322-322+5+2y=0x-322-94+5+2y=0x-322+114+2y=0x-322=-2y+114x-322=-2y+118This is parabola of the typeX2=-4AY4A=2A=12focus, vertex, length of the latus rectum and equation of the directrix fVetex will beX=0 and Y=0x-32=0 and y+118=0x=32 and y=-118Hence vertex is 32,-118Focus isX=0 and Y=-Ax-32=0 and y+118=-12x=32 and y=-118-12=-158Hence focus is 32,-158Length of latus ractum=4A=2 unitsEquation of directrix is:Y=Ay+118=12y=12-118=-711Hence equation of directrix is y=-711

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