SOLUTION: 3. Find the equation of the parabola with latus rectum 6 joining ( -4, 1) and (2, 1).

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Question 1187358: 3. Find the equation of the parabola with latus rectum 6 joining ( -4, 1) and (2, 1).
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

since ( -4, 1) and (2, 1) lie on horizontal line, we need following formula
%28x-h%29%5E2=4p%28y-k%29
given:
Length of latus-rectum is 6 =>4p=6
p=6%2F4
p=3%2F2
plug it in formula
%28x-h%29%5E2=6%28y-k%29
use one endpoint of Latus Rectum to find h and k
(h±2p, k%2Bp)=(2, 1)
h%2B2%283%2F2%29=2-> h=2-3->h=-1
k%2B3%2F2=1 ->k=1-3%2F2->k=-1%2F2

and, your equation is:
%28x%2B1%29%5E2=6%28y%2B1%2F2%29