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September 2nd, 2018, 01:59 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 07:56 AM. 
September 2nd, 2018, 05:39 AM  #2 
Senior Member Joined: May 2016 From: USA Posts: 1,300 Thanks: 549 
Virtual duplicate of post at FMH

September 2nd, 2018, 08:17 AM  #3 
Global Moderator Joined: Dec 2006 Posts: 20,262 Thanks: 1958 
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. 
September 2nd, 2018, 09:26 AM  #4 
Senior Member Joined: Jun 2015 From: England Posts: 891 Thanks: 269 
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. 
September 2nd, 2018, 12:22 PM  #5 
Global Moderator Joined: Dec 2006 Posts: 20,262 Thanks: 1958 
Thanks  I used the wrong factor. I've corrected it to be 3. Note that your $y + 0$ should have been $y  4$. 
September 3rd, 2018, 02:15 AM  #6  
Senior Member Joined: Jun 2015 From: England Posts: 891 Thanks: 269  Quote:
Thanks skip, that's what comes of building up an expression by copy and edit.  
September 3rd, 2018, 03:22 AM  #7 
Global Moderator Joined: Dec 2006 Posts: 20,262 Thanks: 1958  This article provides some background information and another way of obtaining the answer.


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circle, locus, precal, understanding 
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