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If two circles (x+4)^(2)+y^(2)=1 and (x-4)^(2)+y^(2)=9 are touched extermally by a circle, then locus of centre of variable circle is |
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Answer» `(x^(2))/(15)-(y^(2))/(1)=1` `CS=r+1` `CS'=r+3` `CS'-CS=2` Locus of C is hyperbola with `(-4,0)` and `(4,0)` as foci, Here, 2a=2, so a = 1. Also, 2ae = 8, so ae = 4 `therefore""b^(2)=a^(2)(e^(2)-1)=15` |
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