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Free_Kalibri [48]
3 years ago
10

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!
Mathematics
2 answers:
Zigmanuir [339]3 years ago
7 0

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 r.

Katyanochek1 [597]3 years ago
7 0

Answer:

Center// (-5,-6)

Radius// 6

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