My Math Forum intersecting circle formula proof(help)

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 June 7th, 2018, 09:21 PM #1 Newbie   Joined: Jun 2018 From: Mexico Posts: 1 Thanks: 0 intersecting circle formula proof(help) Hi guys, can someone please tell me how to solve this question (Ayres, calculus, 5ed, question 24, chapter 4) let L1 and L2 be two intersecting circles determined by the equations X^2+Y^2+A1X+B1Y+C1=0 and X^2+Y^2+A2X+B2Y+C2=0 for any number k different that -1,show that X^2+Y^2+A1X+B1Y+C1+k(X^2+Y^2+A2X+B2Y+C2 )=0 is the equation of a circle through the intersection points L1 and L2 Last edited by skipjack; June 8th, 2018 at 11:55 PM.
 June 8th, 2018, 04:30 AM #2 Global Moderator   Joined: Dec 2006 Posts: 20,918 Thanks: 2201 Do you see why the points L1 and L2 have coordinates that satisfy the given equation?
 June 8th, 2018, 04:37 PM #3 Global Moderator   Joined: May 2007 Posts: 6,804 Thanks: 715 Do you see that combining the expressions for the circles will end up as an expression for a different circle (if k is not -1)?

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