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A day full of math games & activities. Find one near you.
A day full of math games & activities. Find one near you.
The equation of the parabola whose focus is at (0, 5) and directrix at y = -5 is
Solution:
Given directrix of y = -5 and focus (0,5)
from any point (x, y) on the parabola the focus and directrix are equidistant
We are using distance formula √{(x - 0)2 + (y - 5)2} = |y + 5|
Applying square on both sides
(x)2 + (y - 5)2 = (y + 5)2
(y - 5)2 - (y + 5)2 = -x2
y2 - 10y + 25 - y2 - 10y - 25 = -x2
-20y = -x2
20y = x2
y = x2/20
The quadratic equation created is y = x2/20
The equation of the parabola whose focus is at (0, 5) and directrix at y = -5 is
Summary:
The equation of the parabola whose focus is at (0, 5) and directrix at y = -5 is y = x2 /20.
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