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Point on a line at a given distance from a point, using the parametric (distance) form

This type of question, asked 2 times: 25 Jul 2022, 24 Jan 2026 S2. All 2 questions below, oldest first.

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  1. Question 1

    25 Jul 2022

    72
    A line, with the slope greater than one, passes through the point A(4,3)A(4,3) and intersects the line x−y−2=0x - y - 2 = 0 at the point BB. If the length of the line segment ABAB is 293\frac{\sqrt{29}}{3}, then BB also lies on the line:

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  2. Question 2

    24 Jan 2026 S2

    53
    Let the angles made with the positive x -axis by two straight lines drawn from the point P(2,3)P(2,3) and meeting the line x+y=6x + y = 6 at a distance 23\sqrt{\frac{2}{3}} from the point P be θ1\theta_{1} and θ2\theta_{2}. Then the value of (θ1+θ2)\left( \theta_{1}+\theta_{2} \right) is :

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