Equation of F...

Equation of Family of circles passing through point of intersection of two circles

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Find the equation of family of circles passing through the point of intersection of the circles $x^{2} + y^{2} - 2 x - 4 y - 4 = 0$ and $x^{2} + y^{2} - 10 x - 12 y + 40 = 0$ and whose radius is 4.

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The equation of the circle through the points of intersection of $x^{2} + y^{2} - 1 = 0, x^{2} + y^{2} - 2 x - 4 y + 1 = 0$ and touching the line x + 2y = 0, is

$x^2 + y^2 - x - 2y = 0$

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Q. The equation of the circle passing through (1, 1) and the points of intersection of

x^{2} + y^{2} + 13 x - 3 y = 0

and

2 x^{2} + 2 y^{2} + 4 x - 7 y - 25 = 0

$2 x^{2} + 2 y^{2} + 25 x - 13 y - 30 = 0$
$4 x^{2} + 4 y^{2} + 25 x - 13 y - 30 = 0$
$4 x^{2} + 4 y^{2} + 30 x - 13 y - 25 = 0$
$x^{2} + y^{2} + 15 x - 13 y - 25 = 0$

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The equation of a circle passing through points of intersection of the circles $x^{2} + y^{2} + 13 x - 3 y = 0$ and $2 x^{2} + 2 y^{2} + 4 x - 7 y - 25 = 0$ and point (1, 1) is

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Find the equation of family of circles through the intersection of $x^{2} + y^{2} - 6 x + 2 y + 4 = 0$ and $x^{2} + y^{2} + 2 x - 4 y - 6 = 0$ whose center lies on $y = x .$

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Q. The equation of the circle passing through the point (–2, 4) and through the points of intersection of the circle

x^{2} + y^{2} - 2 x - 6 y + 6 = 0

and the line 3x + 2y - 5 = 0, is

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

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