SOLUTION: Find an equation of the circle with endpoints of a diameter are P(−1, 3) and Q(5, −7)

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Question 941871: Find an equation of the circle with endpoints of a diameter are
P(−1, 3) and Q(5, −7)
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
Find an equation of the circle with endpoints of a diameter are
P(-1, 3) and QP(5, -7)
an equation of the circle is %28x+-h%29%5E2+%2B+%28y+-+k%29%5E2+=+r%5E2; so, we need the coordinates of the center (h+,k) and the radius r
First find the coordinates of the center : (h+,k)
=>+x=h+=+%28x1%2Bx2%29%2F2+=+%28-1%2B5%29+%2F2+=+4%2F2=2
=>+y+=k=+%28y1%2By2%29%2F2+=+%283-7%29+%2F2+=+-4%2F2=-2
so, C (2,-2) is the center
now find the radius ( u can find its length by taking the distance between one endpoint and C )
take (2,-2) and P(-1, 3)
=> r+=+sqrt+%28+%282-1%29%5E2+%2B+%28-2-3%29%5E2+%29+
= >r+=sqrt+%281%2B25%29+
= >r+=sqrt+%2826%29+
= >r+=5.83
hence the equation is :
%28x+-+2%29%5E2+%2B+%28y%2B2%29%5E2+=+26+