Question

If the point P(a, a²) lies completely inside the triangle formed by the lines

x = 0, y = 0 and x + y = 2, then exhaustive range of ‘a’ is –

• A. aÎ (0, 1)
• B. a Î (1, $\sqrt{2}$)
• C. aÎ ($\sqrt{2}$ – 1, $\sqrt{2}$)
• D. a Î ($\sqrt{2}$ – 1, 1)

Answer 1

Answer: (A)

aÎ (0, 1)

Answer 2

x = a y = a² y = x²

x + x² = 2 ̃ x² + x – 2 = 0

x² + 2x – x – 2 = 0

x (x + 2) – 1 (x + 2) = 0

x = –2, 1

For inside the triangle 0 < x < 10 < a < 1