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Q.
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
Conic Sections
Solution:
From the figure, $OB = 1, OD = \frac{1}{\sqrt{2}}$
Also, $OD = \frac{|m(0) - 0 + 1|}{\sqrt{m^2 + 1}}$
So, we have $\frac{|m(0) - 0 + 1|}{\sqrt{m^2 + 1}} = \frac{1}{\sqrt{2}}$
$\therefore m = \pm 1$
