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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

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Solution

The correct option is B

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

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

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Similar questions

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

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

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

(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

(1, 1)

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

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

Find the equation of pair of tangents drawn to the circle $x^{2} + y^{2} - 4 x + 4 y = 0$ from the point (2, 2)

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