My Math Forum Find the diff equation of family of circles with center on t

 Calculus Calculus Math Forum

 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 .
 July 8th, 2013, 05:40 PM #2 Senior Member     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 $(h,-h)$.
 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 $(x- h)^2+ (y+ h)^2= R^2$. The distance from (h, -h) to (0, 0) is, of course, $\sqrt{h^2+ (-h)^2}= h\sqrt{2}$ so $R^2= 2h^2$: $(x- h)^2+ (y+ h)^2= 2h^2$. Multiplying that out, $x^2- 2hx+ h^2+ y^2+ 2hy+ h^2= 2h^2$. Then a wonderful thing happens - all those $h^2$ terms cancel! $x^2+ 2h(y- x)+ y^2= 0$. Now, $h= \frac{x^2+ y^2}{2(y- x)}$. Differentiating with respect to x, the constant, h, will disappear.
 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 $\text{Let circle be centered at (h,-h) and has radius R } (x-h)^2 + (y+h)^2 = R^2 \text{For circle passing via origin, put (0,0) in equation } 2h^2=R^2 \rightarrow (x-h)^2 + (y+h)^2 = 2h^2 x^2 + h^2 -2hx + y^2 + h^2 + 2hy = 2h^2 x^2 + y^2 -2hx + 2hy = 0 h=\frac{x^2+y^2}{2(x-y)}$ @HallsOfIvy : You made a mistake, it should be as above.

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

,

,

,

,

,

,

,

,

,

,

,

,

,

,

# Find the differential equation of the circle haveing centres on the line y x=0 and passing through origin

Click on a term to search for related topics.
 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post fornuftit Algebra 2 May 23rd, 2012 10:23 PM Igo Algebra 2 January 22nd, 2012 07:39 PM Weiler Differential Equations 2 January 16th, 2012 01:38 PM rowdy3 Calculus 2 May 5th, 2010 07:29 PM Igo Calculus 1 December 31st, 1969 04:00 PM

 Contact - Home - Forums - Cryptocurrency Forum - Top