Question

If the chord y = mx + 1 subtends an angle of measure 45⁰ at the major segment of the circle x² + y² = 1 then value of m is-

• A. 1 ±$\sqrt{2}$
• B. –2 ±$\sqrt{2}$
• C. –1 ±$\sqrt{2}$
• D. ± 1

Answer 1

Answer: (D)

± 1

Answer 2

If chord AB y = mx + 1 subtends 45⁰ at the major segment of the circle x² + y² = 1 then it must subtend 90⁰ at the centre (0, 0). The equation of OA and OB,

(by homogenizing), is x² + y² = (y – mx)²

Since OA & OB are perpendicular

Ž coefficient of x² + coefficient of y² = 0

1 – m² + 0 Ž m = ± 1.