Consider the following statements:I. If P(x_1 | vedclass

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(D) Statement $I$: Two points $P(x_1, y_1)$ and $Q(x_2, y_2)$ are conjugate with respect to the circle $x^2+y^2+2gx+2fy+c=0$ if the polar of $P$ passe

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$I$ is true and $II$ is false

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(D) Statement $I$: Two points $P(x_1, y_1)$ and $Q(x_2, y_2)$ are conjugate with respect to the circle $x^2+y^2+2gx+2fy+c=0$ if the polar of $P$ passes through $Q$. The equation of the polar of $P$ is $xx_1+yy_1+g(x+x_1)+f(y+y_1)+c=0$. Substituting $Q(x_2, y_2)$,we get $x_1x_2+y_1y_2+g(x_1+x_2)+f(y_1+y_2)+c=0$. Thus,$I$ is true.Statement $II$: The pole $(x_0, y_0)$ of the line $lx+my+n=0$ with respect to $x^2+y^2=a^2$ is given by $(\frac{-la^2}{n}, \frac{-ma^2}{n})$.For the line $x+y+1=0$ and circle $x^2+y^2=9$,we have $l=1, m=1, n=1, a^2=9$.Pole $= (\frac{-1 	imes 9}{1}, \frac{-1 	imes 9}{1}) = (-9, -9)$.Since the given pole is $(9, 9)$,statement $II$ is false.

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