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Question 539038: im having a difficulty in solving this problem. your help is highly appreciated.
a point moves so that its distance from the point 4,0 is always one half its distance from the line x-16=0. find the equation of its locus
Found 2 solutions by stanbon, Alan3354:
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! a point moves so that its distance from the point 4,0 is always one half its distance from the line x-16=0. find the equation of its locus
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Every point on the line x-16=0 is (16,y) where y can be any Real Number.
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Find distance of (x,y) from (4,0) and from (16,y)
sqrt[(x-4)^2+(y-0)^2] and sqrt[(x-16)^2 + (0)^2]
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Equation:
sqrt[(x-4)^2+(y-0)^2] = (1/2)sqrt[(x-16)^2 + (0)^2]
(x-4)^2+ y^2 = (1/4)(x-16)^2
x^2-8x+16 + y^2 = (1/4)(x^2-32x+256)
etc.
Cheers,
Stan H.
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Answer by Alan3354(69443)  (Show Source):
You can put this solution on YOUR website! The other tutor's solution gives an ellipse, which is obviously not right.
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So far, I get the same answer, tho.
More later.
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Every point that I check on the ellipse fits.
I expected a parabola.
The eqn is 
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