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Consider the following statements :
I. If $P\left(x_1, y_1\right)$ and $Q\left(x_2, y_2\right)$ are conjugate points with respect to the circle $x^2+y^2+2 g x+2 f y+c=0$, then $x_1 x_2+y_1 y_2+g\left(x_1+x_2\right)+f\left(y_1+y_2\right)+c=0$
II. The pole of the line $x+y+1=0$ with respect to the circle $x^2+y^2=9$ is $(9,9)$.
Then, which one of the following is true?
Options:
I. If $P\left(x_1, y_1\right)$ and $Q\left(x_2, y_2\right)$ are conjugate points with respect to the circle $x^2+y^2+2 g x+2 f y+c=0$, then $x_1 x_2+y_1 y_2+g\left(x_1+x_2\right)+f\left(y_1+y_2\right)+c=0$
II. The pole of the line $x+y+1=0$ with respect to the circle $x^2+y^2=9$ is $(9,9)$.
Then, which one of the following is true?
Solution:
2916 Upvotes
Verified Answer
The correct answer is:
I is true and II is false
By definition I statement is true II the pole of line of circle $x^2+y^2=9$ at $(9,9)$ is
$$
9 x+9 y=9 \Rightarrow x+y=1
$$
$\therefore$ II statements is false.
$$
9 x+9 y=9 \Rightarrow x+y=1
$$
$\therefore$ II statements is false.
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