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Question

Let ϕ(x,y)=0 be the equation of a circle, If ϕ(0,λ)=0 has equal roots λ=2,2 and ϕ(λ,0)=0 has roots λ=45,5, then the roots of the circle is


A

(2, 29/100)

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B

(29/10, 2)

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C

(-2, 29/10)

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D

None of these

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Solution

The correct option is B

(29/10, 2)


Let ϕ(x,y)x2+y2+2gx+2fy+c=0ϕ(0,λ)=0+λ2+0+2fλ+c=0
Have equal roots,
Then 2+2=2f1 and 2.2=c1f=2 and c=4and ϕ(λ,0)λ2+0+2gλ+0+c+0λ2+2gλ+c=0Here c=4 λ2+2gλ+4=0have roots 4/5,545+5=2gg=2910

Centre(g,f)=(2910,2)


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