ExamBro
ExamBro
WBJEE · Maths · Hyperbola

The locus of the center of a variable circle which always touches two given circles externally is

  1. A an ellipse
  2. B a hyperbola
  3. C a parabola
  4. D a circle
Verified Solution

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