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If a tangent to the circle x 2 + y 2 = 1 intersects the coordinate axes at distinct points P and Q, then the locus of the mid-point of PQ is :

1. x 2 + y 2 – 2x 2 y 2 = 0
2. x 2 + y 2 – 4x 2 y 2 = 0
3. x 2 + y 2 – 16x 2 y 2 = 0
4. x 2 + y 2 – 2xy = 0

Correct answer: x 2 + y 2 – 4x 2 y 2 = 0

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