+0

0
120
4
+76

The equation for the circle is:

x2+y2+14x+10y−7=0 .

What is the center of the circle?

Acceptfully  May 29, 2017

#1
+4711
+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
Sort:

#1
+4711
+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

Guest May 29, 2017
#3
+4711
+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:

hectictar  May 29, 2017
#4
+1

ok. i get it now thankyou

Guest May 29, 2017

### 24 Online Users

We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details