Class 11

Math

3D Geometry

Conic Sections

Find the centre and radius of the circle $2x_{2}+2y_{2}−x=0$

$⇒(2x_{2}−x)+2y_{2}=0$

$⇒2[(x_{2}−2x )+y_{2}]=0$

$⇒{x_{2}−2x(41 )+(41 )_{2}}+y_{2}−(41 )_{2}=0$

$⇒(x−41 )_{2}+(y−0)_{2}=(41 )_{2}$

which is of the form $(x−h)_{2}+(y−k)_{2}=r_{2}$

where $h=41 $, $k=0$ and $r=41 $

Thus the centre of the given circle is $(41 ,0)$ while its radius is $41 $.