Question

What is the equation of this circle in standard form?
(x − 5.5)2 + (y − 4)2 = 7
(x + 5.5)2 + (y + 4)2 = 3.5
(x − 5.5)2 + (y − 4)2 = 3.5
(x + 5.5)2 + (y + 4)2 = 12.25
(x − 5.5)2 + (y − 4)2 = 12.25

Answer 1

use distance formula to find the radius and the midpoint formula to find the center
then plug them in the standard equation

Answer 2

Is the answer E?

Answer 3

\(\bf (x-{\color{brown}{ h}})^2+(y-{\color{blue}{ k}})^2=r^2
\\ \quad \\ \quad \\
\textit{distance between 2 points}\to radius\to r\\ \quad \\
\begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
M&({\color{red}{ 2}}\quad ,&{\color{blue}{ 4}})\quad N&({\color{red}{ 9}}\quad ,&{\color{blue}{ 4}})
\end{array}\qquad
d = \sqrt{({\color{red}{ x_2}}-{\color{red}{ x_1}})^2 + ({\color{blue}{ y_2}}-{\color{blue}{ y_1}})^2}
\\ \quad \\
\textit{middle point of 2 points }\to center\to ({\color{brown}{ h,k}})\\ \quad \\
\begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
M&({\color{red}{ 2}}\quad ,&{\color{blue}{ 4}})\quad N&({\color{red}{ 9}}\quad ,&{\color{blue}{ 4}})
\end{array}\qquad
\left(\cfrac{{\color{red}{ x_2}} + {\color{red}{ x_1}}}{2}\quad ,\quad \cfrac{{\color{blue}{ y_2}} + {\color{blue}{ y_1}}}{2} \right)\)

Answer 4

\(\bf (x-{\color{brown}{ h}})^2+(y-{\color{brown}{ k}})^2=r^2
\\ \quad \\ \quad \\
\textit{distance between 2 points}\to radius\to r\\ \quad \\
\begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
M&({\color{red}{ 2}}\quad ,&{\color{blue}{ 4}})\quad N&({\color{red}{ 9}}\quad ,&{\color{blue}{ 4}})
\end{array}\qquad
d = \sqrt{({\color{red}{ x_2}}-{\color{red}{ x_1}})^2 + ({\color{blue}{ y_2}}-{\color{blue}{ y_1}})^2}
\\ \quad \\
\textit{middle point of 2 points }\to center\to ({\color{brown}{ h,k}})\\ \quad \\
\begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
M&({\color{red}{ 2}}\quad ,&{\color{blue}{ 4}})\quad N&({\color{red}{ 9}}\quad ,&{\color{blue}{ 4}})
\end{array}\qquad
\left(\cfrac{{\color{red}{ x_2}} + {\color{red}{ x_1}}}{2}\quad ,\quad \cfrac{{\color{blue}{ y_2}} + {\color{blue}{ y_1}}}{2} \right)\)
anyhow, there

Answer 5

Thank you

Answer 6

yw