If a variable line drawn through the intersection of $\frac{x}{\alpha} + \frac{y}{\beta} = 1$ and $\frac{x}{\beta} + \frac{y}{\alpha} = 1$ meets the coordinate axes in A and B, then the locus of the midpoint of AB is
- A. $\alpha \beta (x + y) = xy(\alpha + \beta)$
- B. $\alpha \beta (x + y) = 2xy(\alpha + \beta)$
- C. $(\alpha + \beta)(x + y) = 2\alpha \beta xy$
- D. None of these
✅ Correct Answer: $\alpha \beta (x + y) = 2xy(\alpha + \beta)$
Explanation
By finding the equation of line through the intersection and substituting intercept form, the midpoint locus simplifies to $\alpha \beta (x + y) = 2xy(\alpha + \beta)$.
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