What is the equation of a parable with vertex (2,2) and the directrix is y=2.5?

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Answer 1 · 2016-12-07T09:21:42

The equation is #2y-4=-(x-2)^2#

If the directrix is #y=2.5# and the vertex is #(2,2)#

The line of symmetry is #x=2#

and the focus is #=(2,1.5)#

The distance of a point #(x,y)# on the parabola to the directrix is equal to the distance of that point to the focus.

#2.5-y=sqrt((x-2)^2+(y-1.5)^2)#

#(2.5-y)^2=(x-2)^2+(y-1.5)^2#

#6.25-5y+y^2=(x-2)^2+y^2-3y+2.25#

#4-2y=(x-2)^2#

#2y-4=-(x-2)^2#

graph{(2y-4+(x-2)^2)(y-2.5)=0 [-11.25, 11.25, -5.63, 5.62]}