If the line y=mx +1 meets the circle `x^(2)+y^(2)+3x=0` in two points equidistant and on opposite sides of x-axis, then

Options

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

Answer

B

Explanation

If the line y=mx+1 meets the circle `x^(2)+y^(2)+3x=0` in two points equidistant and on opposite sides of x-axis then the equation `x^(2)+(mx+1)^(2) +3x=0` or `x^(2)(1+m^(2))+(2m+3)x+1=0` must have roots equal in magnitude but opposite in sign.
`:. `Sum of the roots `=0 rArr - (2m+3)/(1+m)=0rArr 2m+3=0`