Answer:
[tex] (x+5)^2 + (y-4)^2 = 49[/tex]
If we compare this equation with the general formula for a circle given by:
[tex] (x-h)^2 +(y-k)^2 = r^2[/tex]
We see that h = -5 and k = 4 so then the center is V = (-5,4). And the radius would be [tex] r = \sqrt{49}= 7[/tex]
Step-by-step explanation:
For this case we have the following expression:
[tex] x^2 + 10 x + y^2 -8y -8 =0[/tex]
We can complete the squares for this case like this"
[tex] [x^2 +10 x +(\frac{10}{2})^2] + [y^2 -8y +(\frac{8}{2})^2] = 8 +(\frac{10}{2})^2 + (\frac{8}{2})^2 [/tex]
And we can express this like that:
[tex] (x^2 +10x + 25) +(y^2 -8y + 16)= 8+ 25+ 16=49[/tex]
And we can simplify like this:
[tex] (x+5)^2 + (y-4)^2 = 49[/tex]
If we compare this equation with the general formula for a circle given by:
[tex] (x-h)^2 +(y-k)^2 = r^2[/tex]
We see that h = -5 and k = 4 so then the center is V = (-5,4). And the radius would be [tex] r = \sqrt{49}= 7[/tex]
