Conversion of [tex]${{x}^{2}}+{{y}^{2}}-4x=0$[/tex] is circle with centre at [tex]$\left( 2,0 \right)$[/tex] and radius [tex]$r=2$[/tex].
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:
[tex]${{\left( x-a \right)}^{2}}+{{\left( y-b \right)}^{2}}={{r}^{2}}$[/tex]
Where [tex](a,b)[/tex] is the coordinates of center of the circle and [tex]r[/tex] is the radius.
Rewrite [tex]${{x}^{2}}+{{y}^{2}}-4x=0$[/tex] in the form of the standard circle equation.
So,
[tex]${{x}^{2}}-4x+{{y}^{2}}=0$[/tex]
Add [tex]$4$[/tex] both sides of the given equation.
[tex]${{x}^{2}}-4x+4+{{y}^{2}}=0+4$[/tex]
[tex]${{\left( x-2 \right)}^{2}}+{{y}^{2}}=4$[/tex]
[tex]${{\left( x-2 \right)}^{2}}+{{\left( y-0 \right)}^{2}}={{\left( 2 \right)}^{2}}$[/tex]
Therefore, the circle properties are,
[tex]$\left( a,b \right)=\left( 2,0 \right)$[/tex]
and [tex]r=2[/tex]
Learn more about circle of polar coordinates here
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