Question

The centre of the circle passing through the points (1, 4), (4, 1) and (–2, 1) is

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

Given :  A circle passing through the points (1, 4), (4, 1) and (–2, 1) is

To find : Center of circle

Solution:

Let say (h , k ) is the center of circle

then (h , k ) will b equidistant from   (1, 4), (4, 1) and (–2, 1)  

=> ( h - 1)² + (k - 4)² = ( h - 4)² + (k - 1)² = (h + 2)² + ( k - 1)²

( h - 4)² + (k - 1)² = (h + 2)² + ( k - 1)²

=> h² - 8h + 16  = h² + 4h + 4

=> 12h = 12

=> h = 1

( h - 1)² + (k - 4)² = ( h - 4)² + (k - 1)²

=> ( 1 - 1)² + (k - 4)² = ( 1 - 4)² + (k - 1)²

=> 0 + k² - 8k + 16 = 9 + k² - 2k + 1

=> 6 = 6k

=> k = 1

Center of circle is ( 1 , 1)

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