# Circle

Write the equation of a circle that passes through the point [0,6] and touch the X-axis point [5,0]:

$(x-x_S)2+(y-y_S)2=r2$

Result

xS =  5
yS =  5.08
r =  5.08

#### Solution:

$S[x_S; y_S] = ?; r=? \ \\ x_S = 5 \ \\ y_S = r \ \\ \ \\ (0 - 5)^2 + (6-y_S)^2 = r^2 = y_S^2 \ \\ y_S = \dfrac{ 5^2 + 6^2 }{ 2 \cdot 6 } = 5.08 \ \\ r = 5.08 \ \\ \ \\ (x-5)^2+(y-5.08)^2=5.08^2$
$r=(5 \cdot \ 5+6 \cdot \ 6)/(2 \cdot \ 6)=5.08$

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