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Hoofbeat
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Could someone help us physicist's with the following question from our Vector Calculus work!!! Thanks :hello:

Two circles have equations:
i) x^2 + y^2 + 2ax + 2by + c=0
ii) x^2 + y^2 + 2a'x + 2b'y + c'=0
Show that these circles are orthogonal if 2aa' + 2bb' = c + c'

Thanks
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evariste
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(Original post by Hoofbeat)
Could someone help us physicist's with the following question from our Vector Calculus work!!! Thanks :hello:

Two circles have equations:
i) x^2 + y^2 + 2ax + 2by + c=0
ii) x^2 + y^2 + 2a'x + 2b'y + c'=0
Show that these circles are orthogonal if 2aa' + 2bb' = c + c'

Thanks
i)=(x+a)^2+(y+b)^2=a^2+b^2-c
ii)=)=(x+a')^2+(y+b')^2=a'^2+b'^ 2-c'
i has centre (-a,-b)
ii has centre if (-a',-b')
distance between centres squared is (-a+a')^2+(-b+b')^2
if circles with rad r,s are orthogonal
then r^2+s^2=d^2 where d=distance between centres (by pythagoras)
so we need
a^2+b^2-c+a'^2+b'^2-c'=(-a+a')^2+(-b+b')^2
=a^2+a'^2-2aa'+b^2+b'^2-2bb'
ie 2aa'+2bb'=c+c'
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Hoofbeat
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Thanks ever so much...we just worked it out that way! Just wasn't sure that that is what we're expected to do as it's from a problem sheet about Vector Calculus so we assumed we should be using grad etc! Oh well, no doubt our tutor will correct us! thanks again...rep coming your way!
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john !!
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what does orthagonal mean?
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