Question

Write the equation of the circle with center (3, 2) and with (9, 3) being a point on the circle. A) (x − 3)2 + (y − 2)2 = 13 B) (x − 3)2 + (y − 2)2 = 18 Eliminate C) (x − 3)2 + (y − 2)2 = 25 D) (x − 3)2 + (y − 2)2 = 37

Answer 1

Check the picture below.

so then, the distance from the center to that point is really the radius.

`\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{3}~,~\stackrel{y_1}{2})\qquad (\stackrel{x_2}{9}~,~\stackrel{y_2}{3})\qquad \qquad d = √(( x_2- x_1)^2 + ( y_2- y_1)^2) \\\\\\ \stackrel{radius}{r}=√((9-3)^2+(3-2)^2)\implies r=√(36+1)\implies r=√(37) \\\\[-0.35em] ~\dotfill`

`\bf \textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \qquad center~~(\stackrel{3}{ h},\stackrel{2}{ k})\qquad \qquad radius=\stackrel{√(37)}{ r} \\\\\\ (x-3)^2+(y-2)^2=(√(37))^2\implies (x-3)^2+(y-2)^2=37`