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The equation for the circle is:

x2+y2+14x+10y−7=0 .

What is the center of the circle?

May 29, 2017

#1
+3

We want to get the equation of the circle into this form:

(x - h)2 + (y - k)2 = r2          , where (h, k) is the center and r is the radius.

x2 + y2 + 14x + 10y - 7 = 0

Subtract 7 from both sides of the equation and rearrange the left side.

x2 + 14x   +   y2 + 10y   =   7

Add (14/2)2 , or 49,   and   (10/2)2 , or 25, to both sides of the equation.

x2 + 14x + 49   +   y2 + 10y + 25   =   7 + 49 + 25

Now we can factor both parts like this

(x + 7)2   +   (y + 5)2   =  81

Now that it is in that form, we can see that the center of the circle is (-7 , -5)

May 29, 2017

#1
+3

We want to get the equation of the circle into this form:

(x - h)2 + (y - k)2 = r2          , where (h, k) is the center and r is the radius.

x2 + y2 + 14x + 10y - 7 = 0

Subtract 7 from both sides of the equation and rearrange the left side.

x2 + 14x   +   y2 + 10y   =   7

Add (14/2)2 , or 49,   and   (10/2)2 , or 25, to both sides of the equation.

x2 + 14x + 49   +   y2 + 10y + 25   =   7 + 49 + 25

Now we can factor both parts like this

(x + 7)2   +   (y + 5)2   =  81

Now that it is in that form, we can see that the center of the circle is (-7 , -5)

hectictar May 29, 2017
#2
+1

where did the 25 come from as well as the 49

May 29, 2017
#3
+2

In order to make   x2 + 14x   a perfect square trinomial, add (14/2)2

x2 + 14x + (14/2)2

x2 + 14x + 72

x2 + 14x + 49

Now it can be factored like this

(x + 7)(x + 7)

(x + 7)2

And whatever you do to one side of the equation, do the same thing to the other side.

So we had to add 49 to both sides. This video might help explain it more:

https://www.youtube.com/watch?v=bNQY0z76M5A hectictar  May 29, 2017
#4
+1

ok. i get it now thankyou

May 29, 2017