The equation of the circle passing through the point of intersection of the circles $x^{2} + y^{2} - 4 x - 2 y = 8$ and $x^{2} + y^{2} - 2 x - 4 y = 8$ and the point $(- 1, 4)$ is

x^{2} + y^{2} + 4 x + 4 y - 8 = 0

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x^{2} + y^{2} - 3 x + 4 y + 8 = 0

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x^{2} + y^{2} + x + y - 8 = 0

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x^{2} + y^{2} - 3 x - 3 y - 8 = 0

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Solution

The correct option is C $x^{2} + y^{2} - 3 x - 3 y - 8 = 0$
Equation of any circle though the points of intersections of given circles is

$x^{2} + y^{2} - 4 x - 2 y - 8 + k (x^{2} + y^{2} - 2 x - 4 y - 8) = 0$ ...... (i)
Since circle Equation (i) passes through $(- 1, 4)$

$(- 1)^{2} + 4^{2} - 4 (- 1) - 2 (4) - 8 + k ((- 1)^{2} + 4^{2} - 2 (- 1) - 4 (4) - 8) = 0$
$∴ k = 1$ , Put this in (i)
$∴$ Required circle is
$x^{2} + y^{2} - 4 x - 2 y - 8 + (1) (x^{2} + y^{2} - 2 x - 4 y - 8) = 0$

$⟹ x^{2} + y^{2} - 3 x - 3 y - 8 = 0$

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The equation of the circle passing through the point of intersection of the circles x2+y2−4x−2y=8 and x2+y2−2x−4y=8 and the point (−1,4) is

The equation of the circle passing through the point of intersection of the circles $x^{2} + y^{2} - 4 x - 2 y = 8$ and $x^{2} + y^{2} - 2 x - 4 y = 8$ and the point $(- 1, 4)$ is