$x^{2} + y^{2} - 2 x - 2 a y - 8 = 0,$ a is a variable. The equation represents a family of circles passing through two fixed points whose coordinates are

(- 2, 0)

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(2, 0)

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(4, 0)

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(- 4, 0)

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Solution

The correct options are
A $(- 2, 0)$
C $(4, 0)$
Equation of the given circle can be written as
$(x^{2} + y^{2} - 2 x - 8) - 2 a (y) = 0$
which represents a family of circles passing through the intersection of the circle $x^{2} + y^{2} - 2 x - 8 = 0$ and the line $y = 0.$
The circle and the line intersect at the points $P (- 2, 0)$ and $Q (4, 0)$ .

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x2+y2−2x−2ay−8=0, a is a variable. The equation represents a family of circles passing through two fixed points whose coordinates are

$x^{2} + y^{2} - 2 x - 2 a y - 8 = 0,$ a is a variable. The equation represents a family of circles passing through two fixed points whose coordinates are