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Nearest and farthest distance of a point from a circle

This type of question, asked 4 times: 21 Apr 2025 S1, 26 Apr 2025 S1, 12 May 2026 S2, 15 May 2026 S2. All 4 questions below, oldest first.

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  1. Question 1

    21 Apr 2025 S1

    147
    The minimum distance and maximum distance of the point P(2,−7)P(2, - 7) from the circle x2+y2−14x−10y−151=0x^{2}+y^{2}- 14x- 10y- 151 = 0 are respectively____\_\_\_\_ units

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  2. Question 2

    26 Apr 2025 S1

    106
    The least distance of the point A(10,7)A(10,7) from the circle x2+y2−4x−2y−20=0x^{2}+y^{2}- 4x- 2y- 20 = 0 is length of seg AM. If MM′MM^{'} is the diameter of the circle, then the lengths of AMAM and AM′AM^{'} are respectively ____\_\_\_\_ , ____\_\_\_\_ units

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  3. Question 3

    12 May 2026 S2

    60
    The length of the tangent segment drawn from point PP to the circle, x2+y2−2x−2y−2=0x^2 + y^2 - 2x - 2y - 2 = 0 is 424\sqrt{2} units. If λmax\lambda_{max} and λmin\lambda_{min} are the maximum and minimum distances of point PP from the circle, then λmax+λmin\lambda_{max} + \lambda_{min} is equal to....

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  4. Question 4

    15 May 2026 S2

    59
    The coordinates of the point on the curve x2+y2=8x^2 + y^2 = 8 which are nearest to the point (2,0)(2, 0) are:

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