Question

The endpoints of the diameter of a circle are (−2, −3) and (4, −1). Which equation represents the circle?

Answer 1

(x − 1)^2 + (y + 2)^2 = 10

Explanation:

Answer 2

The equation of circle is
`(x-1)^(2)`+
`(y-2)^(2)` = 18

Explanation:

Given the endpoints of the diameter of a circle: (-2,-3) and (4,-1)

We know that the equation of circle is

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

where (x,y) is any point on the circle, (h,k) is center of the circle and r is radius of circle.

To find (h,k): the center is midpoint of diameter

Midpoint of diameter with end points (x1,y1) and (x2,y2) is given by

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

(
`(-2+4)/(2)` ,
`(-3-1)/(2)` )

(1,2)

Hence (h,k) is (1,2)

Substituting values of (h.k) and (x.y) as (1,2) and (4,-1) respectively in equation of circle, we get

`(4-1)^(2)` +
`(-1-2)^(2)` =
`r^(2)`

`r^(2)` = 18

Now substituting values of (h,k) and
`r^(2)` in equation of circle, we get

`(x-1)^(2)`+
`(y-2)^(2)` = 18

Hence the equation of circle is
`(x-1)^(2)`+
`(y-2)^(2)` = 18