+884 The center of the circle with equation \(x^2+y^2=-2x-10y-16\) is the point (x,y) . What is x+y?
+13 Sorry Austin, I thought I was deleting my own incorrect answer.
I can't put it back easily. Sorry.
Your answer was mostly good but it did have an error in it. :(
+118609 The center of the circle with equation x^2+y^2=-2x-10y-16 is the point (x,y) . What is x+y?
The question is worded poorly. x and y are variables, not the centre of the circle.
I will call the centre (h,k). These are teh latters most commonly used for this.
\(x^2+y^2=-2x-10y-16\\ x^2+2x\quad +y^2+10y\quad =-16\\ \text{Complete the 2 squares}\\ x^2+2x+1\quad +y^2+10y+25\quad =-16+26\\ (x+1)^2\quad +(y+5)^2\quad =10\\ centre\;\;is\;\;(-1,-5)\\ h+k=-1+-5=-6 \)
