First slide

Analysis of two circles in circles

Question

$If the circumference of the circle x^{2} + y^{2} + 8 x + 8 y - b = 0 is bisected by the circle$ $x^{2} + y^{2} - 2 x + 4 y + a = 0 then a + b =$

Moderate

A

-56
B

58
C

-58
D

54

Solution

$\begin{array}{l} Common chord is 10 x + 4 y - b - a = 0 is passes through (- 4, - 4) \\ \Rightarrow - 40 - 16 = a + b \\ \Rightarrow a + b = - 56 \end{array}$

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