Question

What is the equation of a circle with the center of -2,1 and passes through 3,4

Answer 1

what is the formula of a circle?

Answer 2

you have the center
it passes through 3,4
thus find the radius then
recall that \(\bf (x-{\color{brown}{ h}})^2+(y-{\color{blue}{ k}})^2={\color{purple}{ r}}^2

\qquad center\ ({\color{brown}{ h}},{\color{blue}{ k}})\qquad
radius={\color{purple}{ r}}\)

Answer 3

and thus \(\bf \textit{distance between 2 points}\\ \quad \\
\begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
% (a,b)
&({\color{red}{ -2}}\quad ,&{\color{blue}{ 1}})\quad
% (c,d)
&({\color{red}{ 3}}\quad ,&{\color{blue}{ 4}})
\end{array}\qquad
% distance value
d = \sqrt{({\color{red}{ x_2}}-{\color{red}{ x_1}})^2 + ({\color{blue}{ y_2}}-{\color{blue}{ y_1}})^2}\)

Answer 4

So would it be (x-2)^2 + (x+1) =13

Answer 5

then the equation of circle is (x+2)^2+(y+1)^2=r^2=50
plus because centre is (-2,-1) remember( -*-)=+