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Locus of the midpoint of the segment a moving line cuts off between the axes

This type of question, asked 2 times: 12 Apr 2023, 8 Apr 2026 S2. All 2 questions below, oldest first.

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  1. Question 1

    12 Apr 2023

    78
    If the point (α,733)\left( \alpha,\frac{7\sqrt{3}}{3} \right) lies on the curve traced by the mid-points of the line segments of the lines xcos⁡θ+ysin⁡θ=7,θ∈(0,π2)x\cos\theta + y\sin\theta = 7,\theta \in\left( 0,\frac{\pi}{2} \right) between the coordinates axes, then α\alpha is equal to

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  2. Question 2

    8 Apr 2026 S2

    60
    If a straight line drawn through the point of intersection of the lines 4x+3y−1=04x+ 3y- 1 = 0 and 3x+4y−1=03x+ 4y- 1 = 0, meet the co-ordinate axes at the points P and Q , then the locus of the mid point of PQ is:

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