A certain circle can be represented by the following equation. x2 + y2 + 10x + 12y + 25 = 0. What is the center of this circle? What is the radius of this circle? Please help!

Question

asked Jul 21, 2021 15.6k views

2 Answers

Daniel Schneiter · Answer 1 · 2021-07-22T20:20:38+0000

Let's try to complete the squares.

The x-part starts with
x^2+10x , which is the beginning of
x^2+10x+25=(x+5)^2 . So, we'll think of
x^2+10x as
(x+5)^2-25

Similarly, we have that

y^2+12y = (y+6)^2-36

So, the equation becomes

$x^2 + y^2 + 10x + 12y + 25 = 0 \iff (x+5)^2-25 + (y+6)^2-36+25=0 \iff (x+5)^2+ (y+6)^2-36=0 \iff (x+5)^2+ (y+6)^2=36$

Now we have writte the equation of the circle in the form

(x-k)^2+(y-h)^2=r^2

When the equation is in this form, everything is more simple: the center is
(k,h) and the radius is
.