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Relative position of two circles and the number of common tangents

This type of question, asked 4 times: May 2021 S1, 15 May 2023 S1, 11 May 2024 S1, 19 Apr 2025 S1. All 4 questions below, oldest first.

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  1. Question 1

    May 2021 S1

    109
    The circles x2+y2+6x+6y=0x^2+y^2+6x+6y=0 and x2+y2−12x−12y=0x^2+y^2-12x-12y=0

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  2. Question 2

    15 May 2023 S1

    119
    The number of common tangents to the circles x2+y2−x=0x^{2}+y^{2}-x=0 and x2+y2+x=0x^{2}+y^{2}+x=0 is/are

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  3. Question 3

    11 May 2024 S1

    106
    Number of common tangents to the circles x2+y2−6x−14y+48=0x^2+y^2-6x-14y+48=0 and x2+y2−6x=0x^2+y^2-6x=0 are

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  4. Question 4

    19 Apr 2025 S1

    120
    The number of common tangents that can be drawn to the circles x2+y2−6x=0x^{2}+y^{2}- 6x= 0 and x2+y2+6x+2y+1=0x^{2}+y^{2}+ 6x+ 2y+ 1 = 0 is .

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