Questions in circle

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The circle ${{x}^{2}}+{{y}^{2}}-8x+4y+4=0$ touches
The equation of circle with centre (1, 2) and tangent $x+y-5=0$ is
The equation of the circle passing through the point (–2, 4) and through the points of intersection of the circle ${{x}^{2}}+{{y}^{2}}-2x-6y+6=0$ and the line $3x+2y-5=0$ , is
The equation of the circle of radius 5 and touching the coordinate axes in third quadrant is
The circle ${{x}^{2}}+{{y}^{2}}-3x-4y+2=0$ cuts x-axis at
If ${{g}^{2}}+{{f}^{2}}=c$ , then the equation ${{x}^{2}}+{{y}^{2}}+2gx+2fy+c=0$ will represent
The centre of a circle is (2, –3) and the circumference is $10\pi $ . Then the equation of the circle is
A variable circle passes through the fixed point (2,0) and touches the y-axis . Then the locus of its centre is
The limit of the perimeter of the regular n-gons inscribed in a circle of radius R as $n\to \infty $ is
The centre of circle inscribed in square formed by the lines ${{x}^{2}}-8x+12=0$ and ${{y}^{2}}-14y+45=0$ , is

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