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

The equation ...

Question

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

$4 x^{2} + 4 y^{2} - 30 x - 10 y - 25 = 0$

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

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$4 x^{2} + 4 y^{2} - 17 x - 10 y + 25 = 0$

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$2 x^{2} + 2 y^{2} - 17 x - 10 y + 25 = 0$

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Solution

The correct option is B
$4 x^{2} + 4 y^{2} + 30 x - 13 y - 25 = 0$

Required equation is

$(x^{2} + y^{2} + 13 x - 3 y) + λ (2 x^{2} + 2 y^{2} + 4 x - 7 y - 25) = 0$

which passes through (1, 1), so $λ = \frac{1}{2}$ .

Hence required equation is

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

Suggest Corrections

Similar questions

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

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

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

(1, 1)

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

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

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

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

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

x^{2} + y^{2} + 2 x + 3 y - 7 = 0

x^{2} + y^{2} + 3 x - 2 y - 1 = 0

(1, 2)

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