
PreCalculus PreCalculus Math Forum 
 LinkBack  Thread Tools  Display Modes 
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: 20,655 Thanks: 2087 
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: 20,655 Thanks: 2087 
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, 01:15 AM  #6  
Senior Member Joined: Jun 2015 From: England Posts: 915 Thanks: 271  Quote:
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: 20,655 Thanks: 2087  This article provides some background information and another way of obtaining the answer.


Tags 
circle, locus, precal, understanding 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Locus  evaeva  Complex Analysis  1  July 17th, 2015 01:41 PM 
Locus  Monokuro  Geometry  5  August 2nd, 2014 07:37 PM 
Need help with locus  Goldenglove  Complex Analysis  0  December 15th, 2009 10:12 AM 
LOCUS  symmetry  Algebra  6  January 30th, 2007 02:48 AM 