Question

If the line $(y-2)=m(x+1)$ intersect the circle $x^2+y^2+2x-4y-3=0$ at two distinct points, then the number of possible values of $m$ is

• A. $2$
• B. $1$
• C. any real value of $m$
• D. None of these

Answer 1

Answer: (C)

any real value of $m$

The given line passes through the point $(-1,2)$

Given circle is $S\equiv x^2+y^2+2x-4y-3=0$

Since $S_{(-1,2)}=1+4-2-8-3=-8<0$

$\therefore (-1,2)$ is an interior point of the circle.

Thus $m$ can have any real value.