Mathematics, 08.01.2020 00:31 leapfroggiez
Find the equation of a circle that has the diameter with endpoints a(3,1) and b(7,3) in the coordinate plane
Answers: 2
![\bf ~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ A(\stackrel{x_1}{3}~,~\stackrel{y_1}{1})\qquad B(\stackrel{x_2}{7}~,~\stackrel{y_2}{3}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left( \cfrac{7+3}{2}~~,~~\cfrac{3+1}{2} \right)\implies \left(\cfrac{10}{2}~~,~~\cfrac{4}{2} \right)\implies (5~~,~~2) \\\\[-0.35em] ~\dotfill](/tpl/images/0446/1229/72bab.png)
![\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ A(\stackrel{x_1}{3}~,~\stackrel{y_1}{1})\qquad B(\stackrel{x_2}{7}~,~\stackrel{y_2}{3})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ AB=\sqrt{(7-3)^2+(3-1)^2}\implies AB=\sqrt{4^2+2^2} \\\\\\ AB=\sqrt{20}~\hspace{10em}\stackrel{\textit{radius is half that}}{\cfrac{\sqrt{20}}{2}} \\\\[-0.35em] ~\dotfill](/tpl/images/0446/1229/ccd9d.png)
![\bf \textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \qquad center~~(\stackrel{5}{ h},\stackrel{2}{ k})\qquad \qquad radius=\stackrel{\frac{\sqrt{20}}{2}}{ r} \\\\\\ (x-5)^2+(y-2)^2=\left( \frac{\sqrt{20}}{2} \right)^2\implies (x-5)^2+(y-2)^2=\cfrac{20}{4} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill (x-5)^2+(y-2)^2=5~\hfill](/tpl/images/0446/1229/020a7.png)
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Find the equation of a circle that has the diameter with endpoints a(3,1) and b(7,3) in the coordina...
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