Question

The equation of circle having a diameter with endpoints (-3, 1) and (5, 7) is

A: (x - 4)² + (y - 3)² = 25
B: (x - 1)² + (y - 4)² = 25
C: (x - 1)² + (y - 4)² = 100

Answer 1

find their midpoint, and thus the center of the circle
and use that in the circle formula

Answer 2

\(\textit{middle point of 2 points }\\ \quad \\
\begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
% (a,b)
&({\color{red}{ -3}}\quad ,&{\color{blue}{ 1}})\quad
% (c,d)
&({\color{red}{ 5}}\quad ,&{\color{blue}{ 7}})
\end{array}\qquad
% coordinates of midpoint
\left(\cfrac{{\color{red}{ x_2}} + {\color{red}{ x_1}}}{2}\quad ,\quad \cfrac{{\color{blue}{ y_2}} + {\color{blue}{ y_1}}}{2} \right)
\\ \quad \\ \quad \\


(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

hmmm ohh.. you'd need the radius, of course, well, just find it by getting distance formula, that'd give you the diameter, the radius is half that

Answer 4

okay, thanks :)

Answer 5

\(\textit{distance between 2 points }\\ \quad \\
\begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
% (a,b)
&({\color{red}{ -3}}\quad ,&{\color{blue}{ 1}})\quad
% (c,d)
&({\color{red}{ 5}}\quad ,&{\color{blue}{ 7}})
\end{array}\qquad
% coordinates of midpoint
d = \sqrt{({\color{red}{ x_2}}-{\color{red}{ x_1}})^2 + ({\color{blue}{ y_2}}-{\color{blue}{ y_1}})^2}\)

Answer 6

yw