WBJEE · Maths · Hyperbola
The locus of the center of a variable circle which always touches two given circles externally is
- A an ellipse
- B a hyperbola
- C a parabola
- D a circle
Answer & Solution
Correct Answer
(B) a hyperbola
Step-by-step Solution
Detailed explanation
\(\begin{array}{l} \mathrm{oo}_{1}=\mathrm{r}+\mathrm{r}_{1} \\ \mathrm{oo}_{2}=\mathrm{r}+\mathrm{r}_{2} \\ \therefore \mathrm{oo}_{2}-\mathrm{oo}_{1}=\mathrm{r}_{2}-\mathrm{r}_{1} \end{array}\) hence, locus is hyperbola
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