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Area between x=g(y) and y Axis

If the circle...

Question

If the circle $x^{2} + y^{2} + 4 x + 22 y + l = 0$ bisects the circumference of the circle $x^{2} + y^{2} - 2 x + 8 y - m = 0$ , then $l + m$ is equal to

60

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50

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40

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56

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Solution

The correct option is B $50$
$S_{1} : x^{2} + y^{2} + 4 x + 22 y + l = 0$

$S_{2} : x^{2} + y^{2} - 2 x + 8 y - m = 0$

Since $S_{1}$ bisects the circumference of $S_{2}$ , the common chord will be a diameter of $S_{2}$

$⟹$ Common chord will pass through $C_{2}$

Common chord: $S_{1} - S_{2} = 0$

$⟹ 6 x + 14 y + l + m = 0$

It passes through $C_{2} (1, - 4)$

$⟹ l + m = - 6 (2) - 14 (4) = - 6 + 56$

$l + m = 50$

Suggest Corrections

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