Grade 11Algebra
The circle whose equation are x^2+y^2+c^2=2ax and x^2+y^2+c^2=2by will touch one another externally,if
4 Answers
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Center is same so both the circles can`t touch externally if they are touchimg then they touch infernally
Ajay Pachankar
Here the center are not same of two circle so they can`t touch internally they touch externally but I want this condition what. Is the condition for this
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Approved Tutor Answer8 Years agoSorry there is mistake in my answer, we can write circle equation as (x-a)^2 + y^2 = a^2-c^2 so by this center is (a,0) and radius is √(a^2-c^2) similarly for Nother circle the equation as x^2+(y-b)^2 = b^2-c^2 so the center is (0,b) and radius is √(b^2-c^2) ao if two circles are touching externally then the realtion between them is C1C2=r1+r2 means distance between center = sum of radii of both the circles so by this √(a^2+b^2)=√(a^2-c^2) + √(b^2-c^2) so further if u solve this u will found out that c^2(a^2+b^2)=a^2.b^2 and it equals to 1/c^2= 1/a^2 + 1/b^2.
Samyak Jain
Equation of 1st circle is x2 + y2 – 2ax + c2 = 0.
Let C1 be the centre and r1 be the radius of this circle.
Clearly, C1 
(a,0) & r1 = 
(a2 + 02 – c2) = (a2 – c2)
Equation of 2nd circle is x2 + y2 – 2by + c2 = 0.
Let C2 be the centre and r2 be the radius of this circle.
Clearly, C2 The circles touch each other externally. So, the sum of their radii is equal to the distance between their centres,
i.e., r1 + r2 = C1C2 => (a2 – c2) + (b2 – c2) = 
(a – 0)2 + (0 – b)2
Square both sides => (a2 – c2) + (b2 – c2) + 2(a2 – c2)(b2 – c2) = a2 + b2
2(a2 – c2)(b2 – c2) = 2c2
Again square both sides
a2 b2 = a2 c2 + b2 c2 Divide both sides by a2 b2 c2 , to get
1/c2 = 1/a2 + 1/b2
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