10.1 parabola

Today in class we reviewed parabola 

Parabola: the set of all points (x,y) that are equidistant from a fixed line and a fixed point not on the line.

(X-h)^2=4p(y-k) vertical y= k-p

If p is more than 0, the parabola opens upward. If less than 0, it opens downward.

Focus (h,k+p)

Directrix: y= k-p

Axis of symmetry: x= h

(Y-k)^2=4p (x-h) horizontal 

Focus( k+p, h) 

Directrix: x= h-p

Axis of symmetry: y=k

Now let's see one problem: 

Find th standard form of a parabola with vertex (2,1) and focus (2,4) 

(X-2)^2= 4p (y-1)

P=3

So (x-2)^2=12(y-1)