Find the equation of circle with radius 2 and touching x-axis , such that the centre is in 3rdquadrant, and centre lies on y = 3x

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Please find below the solution to the asked query:

Let equation of cirlce bex2+y2+2gx+2fy+c=0Nowr=2=g2+f2-cg2+f2-c=4....iCentre -g,-f lies on y=3xf=3g....iiAlso circle touches x-axisX intercept in 02g2-c=0g2=c....iiiPut in ic+f2-c=4f=±2But centre lies in third quadrant, hencef=2 -f=-2Put in  ii2=3gg=32c=g2=94We have g,f,c. Put in equation of circle and obtain the equation.

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