(C) The equation of the common chord of two circles $S_1 = 0$ and $S_2 = 0$ is given by $S_1 - S_2 = 0$, provided the coefficients of $x^2$ and $y^2$

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(C) The equation of the common chord of two circles $S_1 = 0$ and $S_2 = 0$ is given by $S_1 - S_2 = 0$, provided the coefficients of $x^2$ and $y^2$ are the same.Given $S_1 = px^2 + py^2 + 2g'x + 2f'y + d = 0$, we first normalize it by dividing by $p$:$\frac{S_1}{p} = x^2 + y^2 + \frac{2g'}{p}x + \frac{2f'}{p}y + \frac{d}{p} = 0$.Now, the equation of the common chord is $\frac{S_1}{p} - S_2 = 0$.Multiplying by $p$, we get $S_1 - pS_2 = 0$.

Class 11 Mathematics 10-1.Circle and System of Circles Chord of contact of tangent and common chord

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Two circles $S_1 = px^2 + py^2 + 2g'x + 2f'y + d = 0$ and $S_2 = x^2 + y^2 + 2gx + 2fy + d' = 0$ have a common chord $PQ$. The equation of $PQ$ is

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A
$S_1 - S_2 = 0$
B
$S_1 + S_2 = 0$
C
$S_1 - pS_2 = 0$
D
$S_1 + pS_2 = 0$

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Chord of contact of tangent and common chord

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Two circles $S_1 = px^2 + py^2 + 2g'x + 2f'y + d = 0$ and $S_2 = x^2 + y^2 + 2gx + 2fy + d' = 0$ have a common chord $PQ$. The equation of $PQ$ is

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