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Tangents to x^2 + y^2 = a^2 with a given slope or intercept condition

This type of question, asked 3 times: 22 Apr 2025 S2, 16 Apr 2026 S1, 19 Apr 2026 S1. All 3 questions below, oldest first.

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  1. Question 1

    22 Apr 2025 S2

    116
    The equations of the tangents to the circle x2+y2=36x^{2}+y^{2}= 36 which are perpendicular to the line 5x+y=25x + y = 2, are

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  2. Question 2

    16 Apr 2026 S1

    58
    The equations of the tangent to the curve x2+y2=10x^2 + y^2 = 10, where the tangent is parallel to the line 2x+y−1=02x + y - 1 = 0, are

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  3. Question 3

    19 Apr 2026 S1

    56
    A line making equal intercepts on coordinate axes and is tangent to the circle x2+y2=4x^2 + y^2 = 4. The length of each intercept made by line on the coordinate axes is ...

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