Question

please help me solve this question​

Answer 1

Heya

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Equation of a circle passing through the points x, y having co-ordinates of center ( h, k ) and radius r is

( x - h )² + ( y - k )² = r²

For point ( 0 , 1 )

Here, x = 0 and y = 1

h² + k² + 1 -2k = r² .... Equation ( i )

For point ( 2 , 3 )

4 + h² - 4h + 9 + k² - 6k = r² ... Equation (ii)

From Equation i and ii

1 - 2k = 13 -4h - 6k

4h + 4k = 12

h + k = 3 .... Equation ( iii )

For point. ( -2 , 5 )

( -2 - h )² + ( 5 - k )² = r²

4 + h² + 4h + 25 + k² - 10k = r² .... Equation ( iv )

From Equation i and iv

1 - 2k = 29 + 4h - 10k

8k - 4h = 28

2k - h = 7 .... Equation ( v )

Now, solve Equation iii and v

we get

h = -1/3

And

k = 10/3

So, the co-ordinates of centre of circle are ( -1/3 , 10/3 )