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30.10.2020 •
Mathematics
What is the equation of a parabola with focus (0,-8) and directrix y=8?
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Ответ:
y = -
x²
Step-by-step explanation:
Any point (x, y) on the parabola is equidistant from the focus and the directrix.
Using the distance formula
Square both sides
x² + (y + 8)² = (y - 8)² ← expand parenthesis on both sides
x² + y² + 16y + 64 = y² - 16y + 64 ( subtract y² - 16y + 64 from both sides )
x² + 32y = 0 ( subtract x² from both sides )
32y = - x² ( divide both sides by 32 )
y = -
x²
Ответ: