Question

Will Give MEDAL

im writing a quiz correction but idk how i got this wrong

What are the coordinates of the center of the circle that passes through the points (1,1)(1,5)(5,5)


(0,0)


(2.5,2.5)

Correct Answer
(3,3)

Incorrect Response
(5,1)



PLZ EXPLAIN

Answer 1

no pic in this one

Answer 2

i thought it was 5,1 because they were the only ones that were in the question
i didn't even think of 3,3

Answer 3

1 More

Answer 4

explain that 2

Answer 5

let the eq. of circle be
where centre is (-g,-f)
\[x^2+y^2+2gx+2fy+c=0 ...(1)\]
because (1,1),(1,5),(5,5) lie on it.
1+1+2g+2f+c=0
or 2g+2f+c=-2 ... (2)
1+25+2g+10f+c=0
or 2g +10f+c =-26 ...(3)
25 +25+10 g+10 f+c=0
10 g+10 f+c=-50 ...(4)
subtract (3) from (2)
-8f=24
g=-3
subtract (4) from (2)
-8g-8f=48
g+f=-6
-3+f=-6
f=-6+3=-3
centre is (3,3)

Answer 6

WOW THANKS !!!!