question_answer

If the line \[y=mx+1\] meets the circle \[{{\text{x}}^{\text{2}}}+{{\text{y}}^{\text{2}}}+\text{3x}=0\]in two points equidistant from and on opposite sides of x-axis, then.     JEE Main  Online Paper (Held On 19  May  2012)

A) 3m+2=0                               

B)                        3m-2=0

C)                        2m+3=0                               

D)                        2m-3=0

Correct Answer: B

Solution :

                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 = (0,) Slope of line, \[m=\tan \theta =\frac{OA}{OB}\] \[\Rightarrow \]\[m=\frac{1}{\frac{3}{2}}=\frac{2}{3}\]\[\Rightarrow \]\[3m-2=0\]