Question

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

• A. $2$
• B. $-2$
• C. $-1$
• D. None of these

Answer 1

The correct option is C $-1$

Given circle is $x^2+y^2=1$

$C(0,0)$ and radius $=1$ and chord is $y=mx+1$
$\cos {45}^o=\frac{CP}{CR}$

$CP=$ perpendicular distance from $(0,0)$ to chord $y=mx+1$
$CP=\frac{1}{\sqrt{m^2+1}}(CR=radius=1)$

$\Rightarrow \cos {45}^o=\frac{1/\sqrt{m^2+1}}{1}$

$\Rightarrow \frac{1}{\sqrt{2}}=\frac{1}{\sqrt{m^2+1}}$

$\Rightarrow m^2+1=2$

$\Rightarrow m=\pm 1$