what is the general equation of the circle whose diameter ends at points (2,3) and (-2,10)

Question

(2,3),(2,-10)

Answer 1

Equation of circle with center (h,k) and radius r:

(x-h)² + (y-k)² = r²

We need to find the center and the radius.

 

The radius is half the diameter.

The diameter is distance from (2,3) to (2,-10)

 

Since the x coordinates are the same the distance

is merely the difference in the y coordinates.

(3-(-10)) = 13 

Radius = d/2 = 6.5

 

To find the center we take the midpoint of the

diameter endpoints.

midpoint of (2,3), (2,-10)

mp = ((2+2)/2, (3-10)/2)

mp = (2, -7/2)

 

the circle has center (h,k) = (2, -7/2) and radius r = 6.5

 

The equation is:

(x-2)² + (y+7/2)² = 6.5²