Let circles $C_{1}$ and $C_{2}$ on Argand plane be given by $|z + 1| = 3$ and $|z - 2| = 7$ respectively. If a variable circle C be such that
it touches $C_{1}$ externally and $C_{2}$ internally .The locus of center of variable circle describes a conic E. If eccentricity of E can be written in simplest from and p/q when p, q
then find the value of |q – p|

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answer is B.

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Detailed Solution

$\sqrt{{(h + 1)}^{2} + k^{2}} = 3 + r a n d \sqrt{{(h - 2)}^{2} + k^{2}} = 7 - r$

Required locus is ellipse

$\sqrt{{(x + 1)}^{2} + y^{2}} + (\sqrt{x - 2)^{2} + y^{2}} = 10$

having focii are

$(- 1, 0) a n d (2, 0)$

$2 a e = 3, e = \frac{3}{10}$

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