If the chord y=mx+1 of the circle x2+y2=1 subtends an angle π4 at the major arc of the circle, then m is

If a chord subtends angle π4 at the arc, then it subtends 2×π4=π2at the centre O.There are only two chords through the point (0,1), namely, y=1+x and y=1−x∴ m=1,−1

If the chord y=mx+1 of the circle x2+y2=1 subtends an angle π4 at the major arc of the circle, then m is

If a chord subtends angle π4 at the arc, then it subtends 2×π4=π2at the centre O.There are only two chords through the point (0,1), namely, y=1+x and y=1−x∴ m=1,−1

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If the chord $y = m x + 1$ of the circle $x^{2} + y^{2} = 1$ subtends an angle $\frac{π}{4}$ at the major arc of the circle, then $m$ is

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-2

$\pm 1$

$\pm \sqrt{2}$

answer is D.

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Detailed Solution

If a chord subtends angle $\frac{π}{4}$ at the arc, then it subtends $2 \times \frac{π}{4} = \frac{π}{2}$ at the centre $O$ .
There are only two chords through the point $(0, 1)$ , namely, $y = 1 + x$ and $y = 1 - x$
$∴ m = 1, - 1$