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

• A. $3m+ 2 = 0$
• B. $3m- 2 = 0$
• C. $2m+ 3 = 0$
• D. $2m-3 = 0$

Answer 1

The Correct Option is B

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, $m = tan\,\theta=\frac{OA}{OB}$ $\Rightarrow m=\frac{1}{3}=\frac{2}{3}$ $\Rightarrow 3m-2=0$