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# circle

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The endpoints of a diameter of a circle are (6,2) and (−4,7) . What is the standard form of the equation of this circle?

Mar 12, 2020

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The endpoints of a diameter of a circle are (6,2) and (−4,7) .

What is the standard form of the equation of this circle?

Center of the circle:

$$\begin{array}{|rcll|} \hline C &=& \dfrac{\binom{6}{2}+\binom{-4}{7}} {2} \\ C &=& \dfrac{\binom{6-4}{2+7}} {2} \\ C &=& \dfrac{\binom{2}{9}} {2} \\ C &=& \binom{1}{4.5} \\ \hline \end{array}$$

The center of the circle is $$(1,~4.5)$$

$$\begin{array}{|rcll|} \hline r^2 &=& (6-1)^2+(2-4.5)^2 \\ r^2 &=& 5^2+(-2.5)^2 \\ r^2 &=& 25 + 6.25 \\ \mathbf{r^2} &=& \mathbf{31.25} \\ \hline \end{array}$$

The equation of this circle: $$\mathbf{(x-C_x)^2 +(y-C_y)^2=r^2 }$$

$$\begin{array}{|rcll|} \hline \mathbf{(x-1)^2 +(y-4.5)^2=31.25 } \\ \hline \end{array}$$

Mar 12, 2020