The center of the circle with equation \(x^2+y^2=-2x-10y-16\) is the point (x,y) . What is x+y?

ant101
Mar 29, 2017

#1**+3 **

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. :(

austinruffino
Mar 29, 2017

#2**+1 **

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.

\(x^2+y^2=-2x-10y-16\\ x^2+2x\quad +y^2+10y\quad =-16\\ \text{Complete the 2 squares}\\ x^2+2x+1\quad +y^2+10y+25\quad =-16+26\\ (x+1)^2\quad +(y+5)^2\quad =10\\ centre\;\;is\;\;(-1,-5)\\ h+k=-1+-5=-6 \)

Melody
Mar 29, 2017