Question 726654
Find an equation of the circle whose diameter has endpoints (1, -5) and (5, -1)
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Standard form of equation for a circle: {{{(x-h)^2+(y-k)^2=r^2}}}, (h,k)=(x,y) coordinates of center, r=radius
use distance formula to find diameter of circle:
diameter=√[(x1-x2)^2+(y1-y2)^2]=√[(5-1)^2+(-1+5)^2]=√[(4)^2+(4)^2]=√32=4√2
radius=2√2
radius^2=8
use end points to find coordinates of center:
midpoint of diameter: (x1+x2)/2, (y1+y2)/2=(5+1)/2, (-1-5)/2=(3,-3)
center: (3,-3)
Equation of given circle: {{{(x-3)^2+(y+3)^2=8}}}