If the circle x² + y² + 2gx + 2fy + c = O bisects the circumference of the circle x² + y² + 2g'x+2f'y + c' = 0 then prove that 2g′(g − g′) + 2ƒ′(ƒ − ƒ') = c − c'

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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 If the circle x\power{2}+y\power{2}+2gx+2fy+c=0 bisects the circumference of the circle
 x\power{2}+y\power{2}+2g'x+2f'y+c'=0 then prove that 2g'(g-g')+2f'(f-f')=c-c'

If
the circle x² + y² + 2gx + 2fy + c = O bisects the circumference of the circle
x² + y² + 2g'x+2f'y + c' = 0 then prove that 2g′(g − g′) + 2ƒ′(ƒ − ƒ') = c − c'
Transcribed Image Text:If the circle x² + y² + 2gx + 2fy + c = O bisects the circumference of the circle x² + y² + 2g'x+2f'y + c' = 0 then prove that 2g′(g − g′) + 2ƒ′(ƒ − ƒ') = c − c'
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