Show that if the point with coordinates (x,y) is equidistant from the point (2,0) and the line y=−4, then y=1/8(x-2)²-2.
1 answer:
Answer:
The demonstration is showed below
Step-by-step explanation:
The distance betwenn two points is given by:
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:
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
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