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June 7th, 2018, 09:21 PM   #1
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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.
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June 8th, 2018, 04:30 AM   #2
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Do you see why the points L1 and L2 have coordinates that satisfy the given equation?
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June 8th, 2018, 04:37 PM   #3
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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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