basic stuff
1.remove parentheses by multiplying factors.
2.use exponent rules to remove parentheses in terms with exponents.
3.combine like terms by adding coefficients.
4.combine the constants
we know the circle's center is at -7, -1, and we know the circle itself passes through 8,7, the distance from the center to a point on it is by definition its radius, therefore
![\bf ~~~~~~~~~~~~\textit{distance between 2 points}\\\\\stackrel{center}{(\stackrel{x_1}{-7}~,~\stackrel{y_1}{-1})}\qquad (\stackrel{x_2}{8}~,~\stackrel{y_2}{7})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}\\\\\\\stackrel{radius}{r}=\sqrt{[8-(-7)]^2+[7-(-1)]^2}\implies r=\sqrt{(8+7)^2+(7+1)^2}\\\\\\r=\sqrt{15^2+8^2}\implies r=\sqrt{225+64}\implies \boxed{r=17}](https://tex.z-dn.net/?f=%20%5Cbf%20~~~~~~~~~~~~%5Ctextit%7Bdistance%20between%202%20points%7D%5C%5C%5C%5C%5Cstackrel%7Bcenter%7D%7B%28%5Cstackrel%7Bx_1%7D%7B-7%7D~%2C~%5Cstackrel%7By_1%7D%7B-1%7D%29%7D%5Cqquad%20%28%5Cstackrel%7Bx_2%7D%7B8%7D~%2C~%5Cstackrel%7By_2%7D%7B7%7D%29%5Cqquad%20%5Cqquad%20d%20%3D%20%5Csqrt%7B%28%20x_2-%20x_1%29%5E2%20%2B%20%28%20y_2-%20y_1%29%5E2%7D%5C%5C%5C%5C%5C%5C%5Cstackrel%7Bradius%7D%7Br%7D%3D%5Csqrt%7B%5B8-%28-7%29%5D%5E2%2B%5B7-%28-1%29%5D%5E2%7D%5Cimplies%20r%3D%5Csqrt%7B%288%2B7%29%5E2%2B%287%2B1%29%5E2%7D%5C%5C%5C%5C%5C%5Cr%3D%5Csqrt%7B15%5E2%2B8%5E2%7D%5Cimplies%20%20r%3D%5Csqrt%7B225%2B64%7D%5Cimplies%20%5Cboxed%7Br%3D17%7D%20)
and since we know that x = -15 for such a point, then
![\bf \textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2\qquad center~~(\stackrel{-7}{ h},\stackrel{-1}{ k})\qquad \qquad radius=\stackrel{17}{ r}\\\\\\\[x-(-7)]^2+[y-(-1)]^2=17^2\implies (x+7)^2+(y+1)^2=289\\\\\\\stackrel{\textit{since we know x = -15}}{(-15+7)^2+(y+1)^2=289}\implies (-8)^2+\stackrel{FOIL}{(y^2+2y+1^2)}=289\\\\\\64+y^2+2y+1=289\implies y^2+2y=224\implies y^2+2y-224=0\\\\\\(y+16)(y-14)=0\implies y=\begin{cases}-16\\14\end{cases}](https://tex.z-dn.net/?f=%20%5Cbf%20%5Ctextit%7Bequation%20of%20a%20circle%7D%5C%5C%5C%5C%20%28x-%20h%29%5E2%2B%28y-%20k%29%5E2%3D%20r%5E2%5Cqquad%20center~~%28%5Cstackrel%7B-7%7D%7B%20h%7D%2C%5Cstackrel%7B-1%7D%7B%20k%7D%29%5Cqquad%20%5Cqquad%20radius%3D%5Cstackrel%7B17%7D%7B%20r%7D%5C%5C%5C%5C%5C%5C%5C%5Bx-%28-7%29%5D%5E2%2B%5By-%28-1%29%5D%5E2%3D17%5E2%5Cimplies%20%28x%2B7%29%5E2%2B%28y%2B1%29%5E2%3D289%5C%5C%5C%5C%5C%5C%5Cstackrel%7B%5Ctextit%7Bsince%20we%20know%20x%20%3D%20-15%7D%7D%7B%28-15%2B7%29%5E2%2B%28y%2B1%29%5E2%3D289%7D%5Cimplies%20%28-8%29%5E2%2B%5Cstackrel%7BFOIL%7D%7B%28y%5E2%2B2y%2B1%5E2%29%7D%3D289%5C%5C%5C%5C%5C%5C64%2By%5E2%2B2y%2B1%3D289%5Cimplies%20y%5E2%2B2y%3D224%5Cimplies%20y%5E2%2B2y-224%3D0%5C%5C%5C%5C%5C%5C%28y%2B16%29%28y-14%29%3D0%5Cimplies%20y%3D%5Cbegin%7Bcases%7D-16%5C%5C14%5Cend%7Bcases%7D%20)
since it's a circle, it touches x = -15 twice, check the picture below.
If i’m understanding this correctly -9 + -4 is equal to -13 so wouldn’t you just add 13 to make it 0?
sorry if this is confusing
Answer:
are you fking retaxrded?
Step-by-step explanation: