Question

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Answer 1

All points (x,y) such that.

Distance from Focus: (x+1)2+(y−4)2−−−−−−−−−−−−−−−√
Distance from Directrix: y−8
Are equal: (x+1)2+(y−4)2−−−−−−−−−−−−−−−√=y−8

A little algebra later...

(x+1)2+(y−4)2=(y−8)2
(x+1)2+(y2−8y+16)=(y2−16y+64)
(x+1)2+(−8y+16)=(−16y+64)
(x+1)2+(16)=(−8y+64)
(x+1)2=(−8y+48)
(x+1)2=−8(y−6)

Vertex: (-1,6)
Distance to Focus: 2
Distance to Directrix: 2

Answer 2

@Sherabartlett
that's pretty much the definition. So yeah. Just fan and medal if that helps.