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  • The distance of the centre of the circle  from the common ch

The distance of the centre of the circle \mathrm{x^2+y^2=2 x} from the common chord of the circles\mathrm{ x^2+y^2+5 x-8 y+1=0} and \mathrm{ x^2+y^2-3 x+7 y-25=0}, is

Option: 1

1


Option: 2

3


Option: 3

2


Option: 4

1/3


Answers (1)

best_answer

The common chord of the circles \mathrm{S=0\, \, and \, \, S^{\prime}=0} is

\mathrm{ \begin{aligned} & S-S^{\prime}=0 \\\\ & \therefore x^2+y^2+5 x-8 y+1-\left(x^2+y^2-3 x+7 y-25\right)=0 \\\\ & \Rightarrow 8 x-15 y+26=0 \end{aligned} }....(i)

The centre of\mathrm x^2+y^2-2 x=0 is (1,0).

The distance of (1,0) from (i) is

\mathrm{ \frac{8+26}{\sqrt{8^2+15^2}}=\frac{34}{17}=2 \text {. } }

 

Posted by

Deependra Verma

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