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Find equation of a circle which touches the y-axis at the origin and passes through the point (b,c)

Find equation of a circle which touches the y-axis at the origin and passes through the point (b,c)

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1 Answers

Soumya Ranjan Mohanty
117 Points
6 years ago
Dear Student,
let eqn of circle is (x-h)^2 + (y-k)^2 = r^2  
As circle touches y axis: (x-h)^2 + (y-k)^2 = h^2 .
It passes through (0,0)=> h^2 + k^2 = h^2 => k=0  
So eqn. Is (x-h)^2 + y^2 =h^2 -----(1)
And it passes through (b,c) so, (b-h)^2 + c^2 = h^2 .
Solving for h, we get h= (b^2 + c^2)/2b , putting value of h in eqn (1): (x-((b^2 + c^2)/2b))^2 + y^2 = ((b^2 + c^2)/2b)^2 ,
=> c^4/(4 b^2) + b^2/4 - (c^2 x)/b - b x + c^2/2 + x^2 + y^2 = c^4/(4 b^2) + b^2/4 + c^2/2. 
Or eqn of circle is   x^2 + y^2 - (c^2 x)/b - b x= 0 [Ans]
 
Thank you,
Soumya Ranjan Mohanty. 

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