If the line $a^2x + ay + 1 = 0$ is normal to the curve $xy = 1$, then
- A. a < 0
- B. 0 < a < 1
- C. a > 0
- D. -1 < a < 1
✅ Correct Answer: a < 0
Explanation
Given curve $xy = 1$ Differentiating $x dy/dx + y = 0$ $dy/dx = -y/x$ Slope of normal $= x/y > 0$ Given line $ay = -a^2x - 1$ Slope $= -a$ So $-a > 0$ Hence $a < 0$
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