Question

The value(s) of 'm' so that the line $y=mx+1$ intersects the circle $x^2+y^2+3x=0$ in two distinct points lying opposite side of the X-axis, can be

• A. $\frac{-3}{2}$
• B. $1$
• C. $10$
• D. $20$

Answer 1

The correct option is A $\frac{-3}{2}$

Given circle'

$x^2+y^2+3x=0$

since y=mx+1

$x^2+(mx+c{)}^2+3x=0$

$x^2(m^2+1)+x(2m+3)+1=0$

In line y=mx+1 meets the circle and equidistant on the opposite side of x-axis

So the equation must have equal roots but of opposite sign

sum of roots=0

$-\frac{2m+3}{m^2+1}=0$

$2m+‘3=0$