Complex NumbersHard
Question
If a variable circle S touches S1 : |z - z1| = r1 internally and S2 : |z - z2| = r2 externally while the curves S1 & S2 touch internally to each other. Then the eccentricity of the locus of the centre of the curve S is equal to
Options
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Solution
c1c2 = r1 - r2
|z1 - z2| = r1 - r2 ..... (1)
cc1 = r1 - r ..... (2)
|z - z1| = r1 - r
cc2 = r + r2
|z - z2| = r + r2 ..... (3)
(2 ) + (3) |z - z1| + |z - z2| = r1 + r2
2a = r1 + r2 |z1 - z2| = 2ae = r1 - r2
e =
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