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#