Question

The locus of the center of a variable circle which cuts-off the intercept of 2 units and 4 units respectively on the X-axis and the Y-axis is .

• A. $y^2-x^2=6$
• B. $y^2-x^2=-6$
• C. $y^2-x^2=-3$
• D. $y^2-x^2=3$

Answer 1

The correct option is D $y^2-x^2=3$

$\mathrm{We}\mathrm{are}\mathrm{given}\mathrm{that}:2\sqrt{g^2-c}=2\mathrm{and}2\sqrt{f^2-c}=4\Rightarrow g^2-c=1\mathrm{and}{f}^2-c=4\Rightarrow f^2-g^2=3\mathrm{Hence}\mathrm{the}\mathrm{locus}\mathrm{of}\mathrm{center}\mathrm{of}a\mathrm{variable}\mathrm{circle}\mathrm{is}:y^2-x^2=3$