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Equation of the tangent at a given point of a circle

This type of question, asked 2 times: 11 May 2023 S1, 16 May 2023 S2. All 2 questions below, oldest first.

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  1. Question 1

    11 May 2023 S1

    138
    The equation of the tangent to the circle, given by x=5cos⁡θx = 5\cos\theta, y=5sin⁡θy = 5\sin\theta at the point θ=π/3\theta = \pi/3 on it, is

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  2. Question 2

    16 May 2023 S2

    135
    One end of the diameter of the circle x2+y2−6x−5y−1=0x^2+y^2-6x-5y-1=0 is (−1,3)(-1,3), then the equation of the tangent at the other end of the diameter is

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