Consider the circles \( x^{2}+y^{2}+3 \sqrt{2}(x+y)=0 \) and \( x^{2}+y^{2}+5 \sqrt{2}(x+y)=0 \). A third circle is drawn internally tangent to larger circle and externally tangent to smaller circle and tangent to their common diameter. If radius of such circle is \( \frac{p}{q} \) ( \( p \& q \) are relatively prime), then value of \( p-q \) is (A) 7 (B) 8 (C) 10 (D) -7

Question

Consider the circles x^2 +y^2 +3√2(x+y) and x^2 +y^2 +5√2(x+y). A third circle is drawn internally tangent to larger circle and externally tangent to smaller circle and tangent to their common diameter. If radius of such circle is \( \frac{p}{q} \) ( \( p \& q \) are relatively prime), then value of \( p-q \) is (A) 7 (B) 8 (C) 10 (D) -7

Answer 1

Correct option is (A) 7