Tangents are drawn to the circle $x^{2} + y^{2} + 6 x + 4 y - 12 = 0$ from origin. Determine the equation of the circle passing through the points of contact of the tangents and the origin.

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Solution

Equation of C.C. of tangents drawn from $(0, 0)$ is
$3 x + 2 y - 12 = 0$
$∴$ Required circle by $S + λ P = 0$ is
$(x^{2} + y^{2} + 6 x + 4 y - 12) + λ (3 x + 2 y - 12) = 0$
Since it passes through $(0, 0) ∴ λ = - 1$ .
$∴$ Circle is $x^{2} + y^{2} + 3 x + 2 y = 0$ .

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