The value of k for which the circle $x^{2} + y^{2} - 4 x + 6 y + 3 = 0$ will bisect the circumference of the circle $x^{2} + y^{2} + 6 x - 4 y + k = 0$ is:

53

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47

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Solution

The correct option is A $53$
Sol The common chord of the two circles is a
diameter of the circle $x^{2} + y^{2} + 6 x - 4 y + x = 0$
equation of the common chord is $10 x - 10 y + (k - 3) = 0$ which passes through
$(3, α)$ if
$10 (- 3) - 10 (2) + (k - 3) = 0$

$K = 53$

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The value of k for which the circle x2+y2−4x+6y+3=0 will bisect the circumference of the circle x2+y2+6x−4y+k=0 is:

The correct option is A 53Sol The common chord of the two circles is a diameter of the circle x2+y2+6x−4y+x=0equation of the common chord is 10x−10y+(k−3)=0 which passes through (3,α) if10(−3)−10(2)+(k−3)=0K=53

The value of k for which the circle $x^{2} + y^{2} - 4 x + 6 y + 3 = 0$ will bisect the circumference of the circle $x^{2} + y^{2} + 6 x - 4 y + k = 0$ is:

The correct option is A $53$
Sol The common chord of the two circles is a
diameter of the circle $x^{2} + y^{2} + 6 x - 4 y + x = 0$
equation of the common chord is $10 x - 10 y + (k - 3) = 0$ which passes through
$(3, α)$ if
$10 (- 3) - 10 (2) + (k - 3) = 0$

$K = 53$