Find The Area Of The Region Satisfying The Inequality $x^2+y^2<=4x+6y+13$ Help, Plz?

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Answer 1 · 2018-02-23T12:03:15

$13pi~~40.8"units"^2$

The function can be rearranged to get:
$f(x,y)<=13$

Now, $f(x,y)<=13$ is just a form of the equation of a circle: $x^2-ax+y^2-by=r^2$

We will ignore what $f(x,y)$ is since that just determines where the centre of the circle is. However, $r$ is the radius of the circle. $r=sqrt(13)$

$"Area of a circle"=pir^2$

$r^2=13$

$"Area"=13pi$

Find The Area Of The Region Satisfying The Inequality x^2+y^2<=4x+6y+13x^2+y^2<=4x+6y+13 Help, Plz?