Math equation help needed

Question

Write the equation of a circle with diameter endpoints of (13, -1) and (-15, 9)

Answer 1

The equation of a circle is:

 

(x-h)² + (y-k)² = r²

• (h,k) is the center of the circle
• r is the radius of the circle

 

So to get the equation you need, you must find the center, (h,k), and the radius, r. 

1. The center is the midpoint of the diameter.  Use the midpoint formula to find the midpoint of the diameter between the two given points, (13,-1) and (-15,9). 
2. Once you have the midpoint, use the distance formula to find the distance between the center and either one of the given points.  That distance is the radius, r.  Now you have (h.k) and r.  Plus them into the equation of the circle above and you're done.

 

Midpoint = ((x₂-x₁)/2, (y₂-y₁)/2) = (h,k)

 

Distance = √((x₂-h)² + (y₂-k)²)