Circles

[ejames2]

There is a circle which meets the following criteria:
a) The center of the circle is the midpoint of the line segment who end points are
(-9.2, 17.3) and (12.4, 11.5)

B. The circle passes through the point (5.8, -2.4)


Can you help me write the exact equation for the circle in standard form.? And help me understand how you did it?

 

[galactus]

Use the midpoint formula to find the radius point of the circle.

\(\displaystyle \L\\\frac{x_{1}+x_{2}}{2}\) and \(\displaystyle \L\\\frac{y_{1}+y_{2}}{2}\)

Once you have that, you'll have the center and a point on the circle.

That's all you need to find the equation.

Use \(\displaystyle (x-h)^{2}+(y-k)^{2}=r^{2}\) to find the radius, where (h,k) is the coordinates of the center you found. x and y are the coordinates of the point on the circle.