Conversion of \(${{x}^{2}}+{{y}^{2}}-4x=0$\) is circle with centre at \($\left( 2,0 \right)$\) and radius \($r=2$\).
What is circle equation?
A circle is a collection of all points in a plane that are evenly spaced. The fixed point is known as the circle's center.
So, the standard equation of a circle is given by:
\(${{\left( x-a \right)}^{2}}+{{\left( y-b \right)}^{2}}={{r}^{2}}$\)
Where \((a,b)\) is the coordinates of center of the circle and \(r\) is the radius.
Rewrite \(${{x}^{2}}+{{y}^{2}}-4x=0$\) in the form of the standard circle equation.
So,
\(${{x}^{2}}-4x+{{y}^{2}}=0$\)
Add \($4$\) both sides of the given equation.
\(${{x}^{2}}-4x+4+{{y}^{2}}=0+4$\)
\(${{\left( x-2 \right)}^{2}}+{{y}^{2}}=4$\)
\(${{\left( x-2 \right)}^{2}}+{{\left( y-0 \right)}^{2}}={{\left( 2 \right)}^{2}}$\)
Therefore, the circle properties are,
\($\left( a,b \right)=\left( 2,0 \right)$\)
and \(r=2\)
Learn more about circle of polar coordinates here
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