Question

What is the general form of the equation of a circle with its center at (-2, 1) and passing through (-4, 1)?

Answer 1

anwsers_

x2 + y2 − 4x + 2y + 1 = 0

x2 + y2 + 4x − 2y + 1 = 0

x2 + y2 + 4x − 2y + 9 = 0

x2 − y2 + 2x + y + 1 = 0

Answer 2

\(\bf \begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
&({\color{red}{ -2}}\quad ,&{\color{blue}{ 1}})\quad &({\color{red}{ -4}}\quad ,&{\color{blue}{ 1}})
\end{array}
\\\quad \\

slope = {\color{green}{ m}}= \cfrac{rise}{run} \implies \cfrac{{\color{blue}{ y_2}}-{\color{blue}{ y_1}}}{{\color{red}{ x_2}}-{\color{red}{ x_1}}}
\\ \quad \\

y-{\color{blue}{ y_1}}={\color{green}{ m}}(x-{\color{red}{ x_1}})\qquad \textit{plug in the values and move everything to the left}\\
\qquad \uparrow\\
\textit{point-slope form}\)