2018 · Q49
It is given that the equations x² - y² = 0 and (x - a)² + y² = 1 have single positive solution. For this, the value of ‘a’ is
Elementary MathematicsGeometry: Lines, Angles and Triangles
- A2√{2}
- B2
- C- 2√{2}
- D1
Explanation
With y = x (first quadrant), the system gives 2x^2 - 2ax + (a^2 - 1) = 0. A single positive solution requires discriminant 8 - 4a^2 = 0 with x = a/2 > 0, i.e. a = sqrt(2). The digitized option B '2' is the damaged rendering of the intended 'sqrt(2)' (compare options A '2sqrt(2)' and C '-2sqrt(2)'), so the keyed letter is B, but this key is disputed. (key disputed)