Question

Find the equation to the circle :
Whose radius is 10 and whose centre is ( - 5, - 6).

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 $(-5,-6)$ and radius is $10$

Hence equation of required circle is given by,

$[x-(-5){]}^2+[y-(-6){]}^2={10}^2$

$\Rightarrow (x+5{)}^2+(y+6{)}^2=100$

$\Rightarrow x^2+10x+25+y^2+12y+36=100$

$\Rightarrow x^2+y^2+10x+12y=39$