Find the equation of the circle passing through the points (1,-2) ,(5,4) and (10,5)
Answers
Given : circle passing through the points (1,-2) ,(5,4) and (10,5)
To Find : Equation of circle.
Solution:
Equation of circle.
(x - h)² + (y - k)² = r²
(1 - h)² + (-2 - k)² = (5 - h)² + (4 - k)² = (10 - h)² + (5 - k)² = r²
(1 - h)² + (-2 - k)² = (5 - h)² + (4 - k)²
=> 1 + h² - 2h + 4 + k² + 4k = 25 + h² - 10h + 16 + k² - 8k
=> 8h + 12k = 36
=> 2h + 3k = 9
(1 - h)² + (-2 - k)² = (10 - h)² + (5 - k)²
=> 1 + h² - 2h + 4 + k² + 4k =100 + h² - 20h + 25 + k² - 10k
=> 18h + 14k = 120
=> 9h + 7k = 60
2h + 3k = 9
9h + 7k = 60
=> h = 9 , k = - 3
(1 - h)² + (-2 - k)² = r²
=> 8² + 1² = r²
=> r² = 65
Hence equation of circle is (x - 9)² + (y +3)² = 65
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