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Equation of a line from the perpendicular distance from the origin and its direction (normal form)

This type of question, asked 4 times: 10 May 2023 S2, 9 May 2024 S2, 20 Apr 2026 S1, 20 Apr 2026 S2. All 4 questions below, oldest first.

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  1. Question 1

    10 May 2023 S2

    139
    If the length of the perpendicular to a line from the origin is 222\sqrt{2} units, which makes an angle of 135∘135^\circ with the X-axis, then the equation of line is

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  2. Question 2

    9 May 2024 S2

    105
    The equation of a line, whose perpendicular distance from the origin is 7 units and the angle which the perpendicular to the line from the origin makes is 120∘120^\circ with positive X-axis, is

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  3. Question 3

    20 Apr 2026 S1

    58
    The area of a triangle formed by a line with the coordinate axes is 4949 sq. units. If the perpendicular drawn from the origin to this line makes an angle of 45∘45^\circ with the positive X-axis, then the equation of line is....

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  4. Question 4

    20 Apr 2026 S2

    55
    A straight line makes equal negative intercepts on the coordinate axes. If the perpendicular distance from the origin to the line is 4 units, then the equation of the line is ......

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