If the chord y = mx + 1 of the circle x2 + y2 = 1 subtends an angle of measure 45° at the major segment of the circle, then the value of m is

Question

If the chord y = mx + 1 of the circle x2 + y2 = 1 subtends an angle of measure 45° at the major segment of the circle, then the value of m is (A) 2 ± √2 (B) -2 ± √2 (C) - 1 ± √2 (D) none of these

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/2ceb159359ca3d69ed1bbb37db5770b2-.png" /> From the figure, OB = 1, OD = (1/√2) Also, OD = (|m(0) - 0 + 1|/√m2 + 1) So, we have (|m(0) - 0 + 1|/√m2 + 1) = (1/√2) ∴ m = ± 1

Q. If the chord $y = m x + 1$ of the circle $x^{2} + y^{2} = 1$ subtends an angle of measure $4 5^{\circ}$ at the major segment of the circle, then the value of $m$ is

$2 \pm 2$

$- 2 \pm 2$

$- 1 \pm 2$

none of these

From the figure, $OB = 1, O D = \frac{1}{2}$
Also, $O D = \frac{∣ m ( 0 ) - 0 + 1∣}{m ^{2} + 1}$
So, we have $\frac{∣ m ( 0 ) - 0 + 1∣}{m ^{2} + 1} = \frac{1}{2}$
$∴ m = \pm 1$

Q. If the chord y=mx+1 of the circle x2+y2=1 subtends an angle of measure 45∘ at the major segment of the circle, then the value of m is

2±2​

−2±2​

−1±2​