Geo5.1.4

Find the focus of the parabola i). $(y-1)^2=8(x-3\,$ . ii). $(y-2)^2=8(x-3)\,$ iii). $y^2-x-2y+2=0\,$

The parabola is in the form

$(y-k)^2=4a(x-h)^2\,$

where $k=1,h=3,a=2\,$

Therefore,the focus is

$(h+a,k)=(5,1)\,$

ii). $(y-2)^2=8(x-3)\,$

$k=2,h=3,a=2\,$

Now the focus is $(h+a,k)=(5,2)\,$

iii). $(y^2-x-2y+2=0\,$

Readjusting the variables

$(y-2)^2-2-x=0\,$

$(y-2)^2=(x+2)\,$

$k=2,h=-2,a=\frac{1}{4}\,$

Focus is

$(-2+\frac{1}{4},2)\,$

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