Question

If the chord $y=mx+1$ of the circle $x^2+y^2=1$ subtends an angle of measure ${45}^{\circ }$ at the major segment of the circle, then the value of $m$ is

• A. $2$
• B. $1$
• C. $-1$
• D. $Noneofthese$

Answer 1

Answer: (B), (C)

The correct options are
B $1$
C $-1$

If chord $y=mx+1$ subtends ${45}^0$ at the major segment of the circle then, it will subtend angle ${90}^0$ at the origin.

Making $x^2+y^2=1$ homogeneous in the second degree with the help of $y=mx+1$, we get

$x^2+y^2=(y-mx{)}^2$

$⟹(1-m^2)x^2+2mxy=0$

for $a{x}^2+b{y}^2+2hxy+2gx+2fy+c=0$ to subtend ${90}^0$ at origin it should satisfy $a+b=0$

$\therefore 1-m^2=0⟹m=\pm 1$