6. Find the equation of circle that passes through the tree points (2,-2), (3,5) and (-4,6) in the plane R2.
Answers
Given : circle passes through the tree points (2,-2), (3,5) and (-4,6)
To find : Equation of circle
Solution:
Let say Equation of circle
(x - h)² + (y - k)² = r²
passes through the tree points (2,-2), (3,5) and (-4,6)
=>(2 - h)² + (-2 - k)² = (3 - h)² + (5 - k)² = (-4 - h)² + (6 - k)²
=> h² - 4h + 4 + k² + 4k + 4 = h² -6h + 9 + k² -10k + 25 = h² + 8h + 16 + k² -12k + 36
=> - 4h + 4k + 8 = -6h -10k + 34 = 8h -12k + 52
- 4h + 4k + 8 = -6h -10k + 34
=> 2h + 14k = 26
=> h + 7k = 13find the equation of circle which passed through origin and cuts off ...
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- 4h + 4k + 8 = 8h -12k + 52
=> -12h + 16k = 44
=> -3h + 4k = 11
3h + 21k = 39
=> 25k = 50
=> k = 2
=> h = - 1
r² = (2 - h)² + (-2 - k)² = 3² + (-4)² = 5²
Equation of circle
(x + 1 )² + (y - 2)² = 5²
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