Equation of F...

Equation of Family of Circles Passing through Point of Intersection of Two Circles

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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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How do you write an equation for a circle whose diameter has endpoints $(- 2, 3)$ and $(4, - 1)$ ?

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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

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

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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 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.

$x^{2} + y^{2} + 2 y + 15 = 0$
$2 x^{2} + 2 y^{2} - 18 x - 22 y + 69 = 0$
$x^{2} + y^{2} - 2 y - 15 = 0$
$x^{2} + y^{2} - 18 x - 22 y + 69 = 0$

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