Question

Circle W has diameter endpoints (- 10, 6) ) and (2, - 8) . What is the equation of the circle W in standard form?

Answer 1

Answer:

The equation of circle W in standard form is $(x+4)^{2}$ +$(y+1)^{2}$ = 85

Step-by-step explanation:

Given the diameter endpoints: (-10,6) and (2, -8)

We know that the equation of circle is given by

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

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

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

( $\frac{-10+2}{2}$  , $\frac{6-8}{2}$  )

(-4,-1)

Hence (h.k) is ( -4,-1)

Substituting values of (h.k) and (x.y) as (-4,-1) and (2,-8) respectively in equation of circle, we get

$(2+4)^{2}$+$(-8+1)^{2}$=$r^{2}$

$r^{2}$ = 85

Substituting the values of (h,k) and $r^{2}$, we get the equation of circle as

$(x+4)^{2}$ +$(y+1)^{2}$ = 85

Hence the equation of circle W in standard form is $(x+4)^{2}$ +$(y+1)^{2}$ = 85