Question

The quadratic equation whose roots are the x and y intercepts of the line passing through (1, 1) and making a triangle of area A with axes may be-

• A. x² + Ax + 2A = 0
• B. x² – 2Ax + 2A = 0
• C. x² – Ax + 2A = 0
• D. None of these

Answer 1

Answer: (B)

x² – 2Ax + 2A = 0

Answer 2

A = $\frac{1}{2}$ × a × b ⇒ ab = 2A

Let equation of line be $\frac{x}{a} + \frac{y}{b} = 1$

Since line passes through (1, 1)

∴ $\frac{1}{a} + \frac{1}{b} = 1$ ⇒ a + b = ab

⇒ a + b = ab = 2A

⇒ Quadratic equation whose roots are a and b

⇒ x² – (a + b)x + ab = 0

⇒ x² – 2Ax + 2A = 0