For what values of $\lambda$ does the equation $6x^2 - xy + \lambda y^2 = 0$ represent two perpendicular lines and lines inclined at angle $\pi/4$
- A. $-6$ and $-35$
- B. $6$ and $1$
- C. $-6$ and $-2$
- D. $-6$ and $1$
✅ Correct Answer: $-6$ and $-35$
Explanation
Given equation $6x^2 - xy + \lambda y^2 = 0$ For perpendicular lines $a + b = 0$ $6 + \lambda = 0$ $\lambda = -6$ For angle $\pi/4$ $\tan(\pi/4) = 1$ Solving gives $\lambda^2 + 36\lambda + 35 = 0$ $\lambda = -1, -35$ Common value $\lambda = -35$
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