167k views
5 votes
Write the equation of the circle with center (3, 2) and (9, 3) a point on the circle.

User Krozero
by
9.2k points

1 Answer

2 votes
so, we know the circle is at (3, 2), and we also know that a point on the circle is at 9,3, well, what is the distance from the center of the circle to any point on the circle? well is just the radius.

Therefore the distance between those two points is the radius, let's check what that is,


\bf ~~~~~~~~~~~~\textit{distance between 2 points}\\ \quad \\ \begin{array}{ccccccccc} &&x_1&&y_1&&x_2&&y_2\\ % (a,b) &&(~{{ 3}} &,&{{ 2}}~) % (c,d) &&(~{{ 9}} &,&{{ 3}}~) \end{array}\qquad % distance value d = \sqrt{({{ x_2}}-{{ x_1}})^2 + ({{ y_2}}-{{ y_1}})^2} \\\\\\ d=√((9-3)^2+(3-2)^2)\implies d=√(6^2+1^2)\implies d=√(37)

now, what is the equation of a circle whose center is at 3,2 and has a radius of √(37)?


\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
User Alan Jay Weiner
by
9.2k points

No related questions found