Geo5.1.4

From Example Problems
Jump to: navigation, search

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)\,

Main Page:Geometry:The Parabola