Find The Area Of The Region Satisfying The Inequality x^2+y^2<=4x+6y+13x2+y24x+6y+13 Help, Plz?

1 Answer
Feb 23, 2018

13pi~~40.8"units"^213π40.8units2

Explanation:

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

Now, f(x,y)<=13f(x,y)13 is just a form of the equation of a circle: x^2-ax+y^2-by=r^2x2ax+y2by=r2

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

"Area of a circle"=pir^2Area of a circle=πr2

r^2=13r2=13

"Area"=13piArea=13π