Class 11

Math

3D Geometry

Conic Sections

Find the equation of the circle with centre $(−a,−b)$ and radius $a_{2}−b_{2} $

Therefore the equation of the circle is

$(x+a)_{2}+(y+b)_{2}=(a_{2}−b_{2} )_{2}$

$⇒x_{2}+2ax+a_{2}+y_{2}+2by+b_{2}=a_{2}−b_{2}$

$⇒x_{2}+y_{2}+2ax+2by+2b_{2}=0$