Question:
If the line $y = mx + 1$ meets the circle $x^2 + y^2 + 3x = 0 $ in two points equidistant from and on opposite sides of $x$-axis, then
If the line $y = mx + 1$ meets the circle $x^2 + y^2 + 3x = 0 $ in two points equidistant from and on opposite sides of $x$-axis, then
Updated On: Jul 28, 2022
- $3m+ 2 = 0$
- $3m- 2 = 0$
- $2m+ 3 = 0$
- $2m-3 = 0$
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The Correct Option is B
Solution and Explanation
Circle: $x^2 + y^2 + 3x = 0$
Centre, $B=\left(-\frac{3}{2}, 0\right)$
Radius $=\frac{3}{2}$ units.
Line : $y=mx+1$
$y$-intercept of the line = 1
$\therefore A= \left(0,1\right)$
Slope of line, $m = tan\,\theta=\frac{OA}{OB}$
$\Rightarrow m=\frac{1}{3}=\frac{2}{3}$
$\Rightarrow 3m-2=0$
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