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September 2nd, 2018, 01:59 AM   #1
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Question Need help understanding Locus

Recently, there's been a lot of suspended classes so topics were rushed, and I'm a 100% sure this wasn't discussed.

Basically, the question is "Find the locus of points three times as far from (0,4) as from (2,0)".

I tried searching up a similar question online, but couldn't find any. From what I understood, from the point (0,4) you basically expand out 3 times, but I don't know what to do next for the point (2,0). Thank you!

Last edited by skipjack; September 2nd, 2018 at 07:56 AM.
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September 2nd, 2018, 05:39 AM   #2
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Virtual duplicate of post at FMH
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September 2nd, 2018, 08:17 AM   #3
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By this formula, √((x - 0)² + (y - 4)²) = 3√((x - 2)² + (y - 0)²).

That simplifies to (x - 9/4)² + (y + 1/2)² = 45/16, which is the equation of a circle.

Last edited by skipjack; September 2nd, 2018 at 12:20 PM. Reason: to correct factor from 4 to 3.
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September 2nd, 2018, 09:26 AM   #4
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Skipjack has used the basic definition of distance between two points and said

Let the locus be all points P (x,y) such that distance from P to (0,4) = 3 times distance from P to (2,0)

But skip I don't understand where the 4 came from?

So I have


$\displaystyle 3\sqrt {{{\left( {x - 2} \right)}^2} + {{\left( {y - 0} \right)}^2}} = \sqrt {{{\left( {x - 0} \right)}^2} + {{\left( {y + 0} \right)}^2}} $

Last edited by studiot; September 2nd, 2018 at 09:41 AM.
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September 2nd, 2018, 12:22 PM   #5
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Thanks - I used the wrong factor. I've corrected it to be 3.

Note that your $y + 0$ should have been $y - 4$.
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September 3rd, 2018, 02:15 AM   #6
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Quote:
Note that your y+0 should have been y−4.
Oops

Thanks skip, that's what comes of building up an expression by copy and edit.
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September 3rd, 2018, 03:22 AM   #7
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This article provides some background information and another way of obtaining the answer.
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