Question

Find the equation to the circle :
Whose radius is a + b and whose centre is (a, - b).

Answer 1

Fact:

Equation of circle with centre $(h,k)$ and having radius $r$ is given by,

$(x-h{)}^2+(y-k{)}^2=r^2$

Here, centre is $(a,-b)$ and radius is $a+b$

hence equation of required circle is given by,

$(x-a{)}^2+[y-(-b){]}^2=(a+b{)}^2$

$\Rightarrow (x-a{)}^2+(y+b{)}^2=a^2+b^2+2ab$

$\Rightarrow x^2-2ax+a^2+y^2+2by+b^2=a^2+b^2+2ab$

$\Rightarrow x^2+y^2-2ax+2by=2ab$