The equation of circle having a diameter with endpoints (-2, 1) and (6, 7) is (x - 4)² + (y - 3)² = 25 (x - 2)² + (y - 4)² = 25 (x - 2)² + (y - 4)² = 100

Determine the equation of circle having a diameter with endpoints (-2, 1) and (6, 7)

x1 = -2

x2 = 6

y1 = 1

y2 = 7

Midpoint formula:

( x1 + x2)/2 , (y1 + y2)/2

Use the midpoint formula to determine the center of the circle.

Distance formula:

d=√((x2 - x1)²+(y2 - y1)²)

Once the midpoint is located, we can use the distance formula to determine the radius of the circle.

Solution:

Find first the midpoint:

= ( -2 + 6)/2, (1 + 7)/2

= 4/2, 8/2

Center of the circle= (2, 4)

Now that we have the center of the circle, we can find the radius by using the distance formula.

d=√((6- (-2))²+(7 - 1)²)

d=√((8)²+(6)²)

d=√(64 + 36)

d=√(100)

d = 10

r = 10

Equation of the circle with the center at the origin (0,0)

x^2 + y^2 = r^2

Equation of the circle with center at any point (h,k)

(x - h)^2 + ( y - k )^2 = r^2

Since we have two points, then we will use the second equation.

( x -  2 )^2 + ( y - 4 )^2 = 10^2

( x -  2 )^2 + ( y - 4 )^2 = 100

Final answer:

( x -  2 )^2 + ( y - 4 )^2 = 100