My Math Forum Need help understanding Locus

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 September 2nd, 2018, 12:59 AM #1 Newbie   Joined: Sep 2018 From: Philippines Posts: 1 Thanks: 0 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 06:56 AM.
 September 2nd, 2018, 04:39 AM #2 Senior Member   Joined: May 2016 From: USA Posts: 1,310 Thanks: 551 Virtual duplicate of post at FMH
 September 2nd, 2018, 07:17 AM #3 Global Moderator   Joined: Dec 2006 Posts: 20,972 Thanks: 2222 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 11:20 AM. Reason: to correct factor from 4 to 3.
 September 2nd, 2018, 08:26 AM #4 Senior Member   Joined: Jun 2015 From: England Posts: 915 Thanks: 271 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 08:41 AM.
 September 2nd, 2018, 11:22 AM #5 Global Moderator   Joined: Dec 2006 Posts: 20,972 Thanks: 2222 Thanks - I used the wrong factor. I've corrected it to be 3. Note that your $y + 0$ should have been $y - 4$. Thanks from studiot
September 3rd, 2018, 01:15 AM   #6
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Joined: Jun 2015
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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.

 September 3rd, 2018, 02:22 AM #7 Global Moderator   Joined: Dec 2006 Posts: 20,972 Thanks: 2222 This article provides some background information and another way of obtaining the answer.

 Tags circle, locus, precal, understanding

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