Question 1190865: Find the equation of a parabola with axis parallel to Ox and passing through (5, 4), (11, 2), and (21, -4).
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! Find the equation of a parabola with axis parallel to Ox and passing through
(5,4), (11,2), and (21,-4).
If "parallel to Ox" means parallel to the x-axis:
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Parabolas parallel to the x-axis have the form:
x = ay^2 + by + c
------------
5 = a*4^2 + b*4 + c at (5,4)
11= a*2^2 + b*2 + c at (11,2)
21= a*4^2 + b*-4 + c at (21,-4)
------
16a + 4b + c = 5 Eqn 1
4a + 2b + c = 11 Eqn 2
16a - 4b + c = 21 Eqn 3
---
16a + 4b + c = 5 Eqn 1
16a - 4b + c = 21 Eqn 3
----------------------------- Add
32a + 2c = 26 Eqn A
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16a + 4b + c = 5 Eqn 1
8a + 4b + 2c = 22 Eqn 2 times 2
----------------------------------------- Subtract
8a - c = -17
16a + c = 13 Eqn A divided by 2
------------------------------------------ Add
24a = -4
a = -1/6
============
16a + c = 13 Eqn A divided by 2
-8/3 + c = 13
c = 47/3
=================
4a + 2b + c = 11 Eqn 2
-2/3 + 2b + 47/3 = 11
2b = -4
b = -2
=================
--> x = -y^2/6 - 2y + 47/3
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