1.

Prove that the locus of centre of the circle which toches two given disjoint circles externally is hyperbola.

Answer»

Solution :As SHOWN in the figure, variable circle S with centre C and RADIUS r touches two GIVEN disjoint CIRCLES `S_(1)` and `S_(2)` having centres `C_(1)` and `C_(2)` and radii `r_(1)` and `r_(2)`, respectively.

Clearly, `"CC"_(1)=r+r_(1) and "CC"_(2)=r+r_(2)`
`therefore"CC"_(1)-"CC"_(2)=r_(1)-r_(2)(="constant")`
Thus, LOCUS of centre C is hyperbola having foci `C_(1) and C_(2)`.


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