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Director Circle

The distance ...

Question

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

A

2

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B

4

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C

\frac{34}{13}

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D

\frac{26}{17}

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Solution

The correct option is B $2$
Centre of the circle $x^{2} + y^{2} = 2 x$ is $(1, 0)$ .
Common chord of the other two circles is
$8 x - 15 y + 26 = 0$
Distance from $(1, 0)$ to $8 x - 15 y + 26 = 0$
$\frac{| 8 + 26 |}{\sqrt{15^{2} + 8^{2}}} = 2$

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