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A line segment AB of length ‘2’ moves with its ends on the axes. The locus of the point P which divides the segment in the ratio 1:1 is

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$9 x^{2} + 9 y^{2} = 4$

$x^{2} + 4 y^{2} = 8$

$9 x^{2} + 4 y^{2} = 1$

$x^{2} + y^{2} = 1$

answer is B.

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Detailed Solution

$\begin{array}{l} A (α, 0) B (0, β) \\ \Rightarrow P (x, y) = Midpoint of AB \\ \Rightarrow (x, y) = (\frac{α}{2}, \frac{β}{2}) ΔABC \\ α = 2 x β = 2 y \end{array}$

Substitute in $α^{2} + β^{2} = 4$

$4 x^{2} + 4 y^{2} = 4 x^{2} + y^{2} = 1$

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