write an equation of a circle whose endpoints of a diameter are (-1,2) and (5,6)

Question

endpoints of a diameter are (-1,2) and (5,6)

Answer 1

The equation of a circle is:

 

(x-h)² + (y-k)² = r²

 

where (h,k) is the location of the circle's center and r is the circle's radius.  To find the equation, you need to find the values of h, k, and r. Here's how you do it:

 

To find the center, used the midpoint formula to find the midpoint of the given diameter.  The midpoint is the circle's center (the x coordinate = h, the y-coordinate = k).

 

To find the radius (r), use the distance formula to find the distance from the midpoint (center) to either endpoint of the given diameter.  That distance is the radius r.

 

You can look up the midpoint and distance formulas in your textbook or google them on the internet.