How to Find Equation of a Circle Passing 3 Given Points
7 methods included ; Amazing !!
Practice finding the equation of a Circle given 3 points --
Answer : (x -4)2 + y2 = 18
Q #2 : (3, 4), (3, -4), (0, 5)
Answer : x2 + y2 = 25
Q #3 : A (1, 1), B (2, 4), C (5, 3)
Answer : (x-3)2 + (y -2)2 = 5
Solution :
The midpoint of line AB on the Cartesian plane is \((\frac{3}{2}, \frac{5}{2})\) and the slope is \((\frac{3}{1})\) so the slope of the perpendicular bisector of line AB is \((\frac{-1}{3})\).
The equation of the line bisect line AB and perpendicular to line AB is thus :
y - \((\frac{5}{2}\)) =\(\frac{-1}{3}\) [x - \((\frac{3}{2})\)] --- equation 1
The midpoint of line BC on the Cartesian plane is \((\frac{7}{2}, \frac{7}{2})\) and the slope is \((\frac{-1}{3})\) so the slope of the perpendicular bisector of line BC is 3.
And the equation of the line bisect line BC and perpendicular to line BC is
y - \((\frac{7}{2})\) = 3 [x - \((\frac{7}{2})\)] --- equation 2
Solve the two equations for x and y and you have the center of the circle being (3, 2)
Use distance formula from the center circle to any point to get the radius =
\(\sqrt{5}\).More practices on similar questions : (Answers below for self check)
Q #1 : A (2, 5) , B (2, 13) , and C (-6, 5 )
Q #3 : A (3, -5) , B (-4, 2) and C (1, 7 )
Answer key :
#1 : (x - 2) 2 + ( y - 9 ) 2 = 32
#2 : x2 + (y + 3)2 = 100
#3 : (x - 2) 2 + ( y -1) 2 = 37
