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Range of the constant for which a circle does not meet the axes or lies in one quadrant

This type of question, asked 2 times: 2021 Paper 13, 27 Jun 2022. All 2 questions below, oldest first.

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  1. Question 1

    2021 Paper 13

    52
    If 36x2+36y2−108x+120y+C=036x^{2}+ 36y^{2}- 108x+ 120y+C= 0, the circle does not cut/touch coordinate axis. Find the range of CC.

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  2. Question 2

    27 Jun 2022

    162
    The set of values of kk for which the circle C : 4x2+4y2−12x+8y+k=04x^{2}+ 4y^{2}- 12x + 8y + k = 0 lies inside the fourth quadrant and the point (1,−13)\left( 1, -\frac{1}{3} \right) lies on or inside the circle CC is :

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