Question

The distance between the internal and external centres of similitude with respect to the circles \[ x^2+y^2+4x+6y+12=0 \] and \[ x^2+y^2-6x-4y+9=0 \] is:

• A. \(5\sqrt{2}\)
• B. \(\dfrac{20\sqrt{2}}{3}\)
• C. \(16\)
• D. \(5\)

Hint:

For two circles with radii \(r_1\) and \(r_2\) and centre distance \(d\), remember the shortcut \[ \text{Distance between internal and external centres of similitude} = \frac{2r_1r_2d}{|r_1^2-r_2^2|}. \] This avoids finding the centres of similitude individually.

Answer 1

The Correct Option is B