SOLUTION: Find the equation of the parabola with latus rectum 6 joining ( -4, 1) and (2, 1).

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Question 1190796: Find the equation of the parabola with latus rectum 6 joining ( -4, 1) and (2, 1).
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

the equation of the parabola with latus rectum +6 joining (+-4, 1) and (2, 1)
Length of latus rectum is +6, so the leading coefficient is ±1%2F6
y+=+%281%2F6%29%28x-h%29%5E2%2Bk
calculate h and k
use (+-4, 1)
1+=+%281%2F6%29%28-4-h%29%5E2%2Bk
k+=+1%2F6+%28-h%5E2+-+8+h+-+10%29...........eq.1

and (2, 1)
1+=+%281%2F6%29%282-h%29%5E2%2Bk
k+=++-h%5E2%2F6+%2B+%282+h%29%2F3+%2B+1%2F3...........eq.2
then, from eq.1 and eq.2 we have
1%2F6+%28-h%5E2+-+8+h+-+10%29=-h%5E2%2F6+%2B+%282+h%29%2F3+%2B+1%2F3
-2h+-+2+=+0
h=-1
go to
k+=+1%2F6+%28-h%5E2+-+8+h+-+10%29...........eq.1, substitute h
k+=+1%2F6+%28-%28-1%29%5E2+-+8+%28-1%29+-+10%29=-1%2F2

and, your equation is:
y+=+%281%2F6%29%28x%2B1%29%5E2-1%2F2