Since, perpendicular distance from centre of the circle to the common tangent is equal to radius of the circle,
√5
m
√1+m2
=√
5
2
On squaring both the side, we get m2(1+m2)=2 ⇒m4+m2−2=0 ⇒(m2+2)(m2−1)=0 ⇒m=±1(∵m2≠−2) y=±(x+√5), both statements are correct as m=±1 satisfies the given equation of statement- 2 .