Answer:
The demonstration is showed below
Step-by-step explanation:
The distance betwenn two points is given by:
[tex]d = \sqrt{(x2-x1)^2+(y2-y1)^2}[/tex]
If the point is equidistant from a point and a line, the distance must be equal. For the line let's select the point (x,-4), because the distance will be ortogonal, and is the small distance between a point and a line. So:
[tex]\sqrt{(x-2)^2+(y-0)^2} = \sqrt{(x-x)^2+(y+4)^2}[/tex]
Removing the squares:
(x-2)² + y² = (y+4)²
(x-2)² + y² = y² + 8y + 16
y² - y² - 8y = 16 - (x-2)²
8y = (x-2)² - 16
y = (1/8)*(x-2)² - 16/8
y = (1/8)*(x-2)² - 2
