Equation of Circle Touches Both Axes

In this tutorial find of circle which touches both axis i.e. X-axis and Y-axis with any given radius, so can be find equation of circle in the all four quadrants.


equation-cirlce-touches-axes

Let equation of required circle having center and radius

{\left(  {x - h} \right)^2} + {\left( {y - k} \right)^2} = {r^2}\,\,\,{\text{ - - -  }}\left( {\text{i}} \right)


In First Quadrant:
In the first quadrant equation of circle can be finding by using center {C_1}\left( {r,r} \right) and radius is equal to r, equation (i) becomes

{\left(  {x - r} \right)^2} + {\left( {y - r} \right)^2} = {r^2}


In Second Quadrant:
In the second quadrant equation of circle can be finding by using center {C_2}\left( { - r,r} \right) and radius is equal to r, equation (i) becomes

{\left(  {x + r} \right)^2} + {\left( {y - r} \right)^2} = {r^2}


In Third Quadrant:
In the third quadrant equation of circle can be finding by using center {C_3}\left( { - r, - r}  \right) and radius is equal to r, equation (i) becomes

{\left(  {x + r} \right)^2} + {\left( {y + r} \right)^2} = {r^2}


In Forth Quadrant:
In the forth quadrant equation of circle can be finding by using center {C_4}\left( {r, - r} \right) and radius is equal to r, equation (i) becomes

{\left(  {x - r} \right)^2} + {\left( {y + r} \right)^2} = {r^2}

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