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Angle between Two Lines

If a variable...

Question

If a variable circle $S$ touches $S_{1} : | z - z_{1} | = r_{1}$ internally and $S_{2} : | z - z_{2} | = r_{2}$ externally while the curves $S_{1} a n d S_{2}$ touch internally to each other. Then the eccentricity of the locus of the centre of the curve $S$ is equal to

A

\frac{r_{1}}{r_{2}}

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B

\frac{r_{2}}{r_{1}}

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C

\frac{r_{1} + r_{2}}{r_{1} - r_{2}}

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D

\frac{r_{1} - r_{2}}{r_{1} + r_{2}}

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Solution

The correct option is D $\frac{r_{1} - r_{2}}{r_{1} + r_{2}}$

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