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Tangent Circles

If the circum...

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 equals to

50

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56

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- 56

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- 34

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Solution

The correct option is B $- 56$
Equation of radical axis (i.e. common chord) of the two circles is
$10 x + 4 y - a - b = 0$ ...... (i)
Centre of first circle is $H (- 4, - 4)$
Since second circle bisects the circumference of the first circle, therefore, centre $H (- 4, - 4)$ of the first circle must lie on the common chord Equation (i).
$∴ - 40 - 16 - a - b = 0$
$\Rightarrow a + b = - 56$

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