Question

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

Answer 1

Answer:

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

Step-by-step 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

(  $\frac{x1+x2}{2}$ , $\frac{y1+y2}{2}$  )

( $\frac{-2+4}{2}$ , $\frac{-3-1}{2}$  )

(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

Answer 2

Answer:

(x − 1)^2 + (y + 2)^2 = 10

Step-by-step explanation: