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If the line $y=m x+1$ meets the circle $x^2+y^2+3 x=0$ in two points equidistant from and on opposite sides of $x$-axis, then
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Verified Answer
The correct answer is:
$3 m-2=0$
$3 m-2=0$
Circle: $x^2+y^2+3 x=0$
Centre, $B=\left(-\frac{3}{2}, 0\right)$
$y$-intercept of the line $=1$
$$
\therefore \quad \mathrm{A}=(0,1)
$$
Slope of line, $m=\tan \theta=\frac{O A}{O B}$
$$
\begin{aligned}
& \Rightarrow m=\frac{1}{\frac{3}{2}}=\frac{2}{3} \\
& \Rightarrow 3 m-2=0
\end{aligned}
$$
Centre, $B=\left(-\frac{3}{2}, 0\right)$
$y$-intercept of the line $=1$
$$
\therefore \quad \mathrm{A}=(0,1)
$$
Slope of line, $m=\tan \theta=\frac{O A}{O B}$
$$
\begin{aligned}
& \Rightarrow m=\frac{1}{\frac{3}{2}}=\frac{2}{3} \\
& \Rightarrow 3 m-2=0
\end{aligned}
$$
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