Question

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

Answer 1

`(x-2)^(2)+(y-4)^(2)=25`

Explanation:

step 1

Find the diameter of the circle

the formula to calculate the distance between two points is equal to

`d=\sqrt{(y2-y1)^(2)+(x2-x1)^(2)}`

`A(-2,1)\\B(6,7)`

substitute the values

`d=\sqrt{(7-1)^(2)+(6+2)^(2)}`

`d=\sqrt{(6)^(2)+(8)^(2)}`

`d=√(100)`

`d=10\ units`

The radius is half the diameter

so

`r=10/2=5\ units`

step 2

Find the center of the circle

the center of the circle is the midpoint between the endpoints of the diameter

so

The center is

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

`(2,4)`

step 3

Find the equation of the circle

The equation of the circle is

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

substitute the values

`(x-2)^(2)+(y-4)^(2)=5^(2)`

`(x-2)^(2)+(y-4)^(2)=25`