My Math Forum  

Go Back   My Math Forum > College Math Forum > Calculus

Calculus Calculus Math Forum


Reply
 
LinkBack Thread Tools Display Modes
July 8th, 2013, 04:24 PM   #1
Member
 
Joined: Jun 2013

Posts: 42
Thanks: 0

Find the diff equation of family of circles with center on t

Find the diff equation of family of circles with center on the line y= -x and passing through the origin.

I'm good in differentiating... but my problem is that if the equation to be differentiated is not given at the start like this worded problem... I know that the eq of circle. is (x-h)^2 + (y-k)^2 =r^2.... but I don't know how to use the given... line y=-x ..... and how to substitute this given line in this equation... can someone give me the proper equation for this problem??.. don't worry I just need the first equation... I will be the one to differentiate .
gen_shao is offline  
 
July 8th, 2013, 05:40 PM   #2
Senior Member
 
MarkFL's Avatar
 
Joined: Jul 2010
From: St. Augustine, FL., U.S.A.'s oldest city

Posts: 12,211
Thanks: 521

Math Focus: Calculus/ODEs
Re: Find the diff equation of family of circles with center

I would try letting the center of the circle be .
MarkFL is offline  
July 9th, 2013, 11:46 AM   #3
Math Team
 
Joined: Sep 2007

Posts: 2,409
Thanks: 6

Re: Find the diff equation of family of circles with center

A circle with center at (h, -h) (on y= -x as MarkFL suggests, would have equation of the form . The distance from (h, -h) to (0, 0) is, of course, so : . Multiplying that out, .

Then a wonderful thing happens - all those terms cancel! . Now, . Differentiating with respect to x, the constant, h, will disappear.
HallsofIvy is offline  
July 9th, 2013, 12:52 PM   #4
Senior Member
 
Joined: Aug 2012
From: New Delhi, India

Posts: 157
Thanks: 0

Re: Find the diff equation of family of circles with center


@HallsOfIvy : You made a mistake, it should be as above.
Rejjy is offline  
Reply

  My Math Forum > College Math Forum > Calculus

Tags
center, circles, diff, equation, family, find



Search tags for this page
Click on a term to search for related topics.
Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Find center of a circle fornuftit Algebra 2 May 23rd, 2012 10:23 PM
Find center, radius, x-intercept, y-intercept of the circles Igo Algebra 2 January 22nd, 2012 07:39 PM
Differential Equation. Orthogonal Family Weiler Differential Equations 2 January 16th, 2012 01:38 PM
Find the center, vertices, foci and eccentricity rowdy3 Calculus 2 May 5th, 2010 07:29 PM
Find center and radius Igo Calculus 1 December 31st, 1969 04:00 PM





Copyright © 2019 My Math Forum. All rights reserved.