SOLUTION: I managed to do 7,8 :D just now, something clicked :D But, question 9, IMPOSSIBLE :P im so awful haha! :D Find the equation of the circles passing through these sets of point

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Question 122054This question is from textbook AS core for edexcel, advanced maths.
: I managed to do 7,8 :D just now, something clicked :D
But, question 9, IMPOSSIBLE :P im so awful haha! :D
Find the equation of the circles passing through these sets of points.
a ( 5,0), (3,4) and ( -5,0)
b. (6,3), (-5,2) and (7,2)
c. (2,0), (3,1) and (-6,10)
if some one could help me with those three, id actually be so amazingly happy :D
ill forget the rest :P this is just like the hardest thing ive done :D :( please help :D This question is from textbook AS core for edexcel, advanced maths.

Answer by solver91311(24713) (Show Source):
You can put this solution on YOUR website!
I'm just going to tell you what you need to do. If you still can't figure it out after that, write back.

Label your points , , and .

Use the two-point form of the straight line to create the equation for the line containing and , to obtain the slope of the line. The segment forms a chord of the desired circle. A perpendicular to a chord passing through the mid-point of the chord passes through the center of the circle. Determine the mid-point of using the mid-point formula: and . Recalling that slopes of perpendicular lines are negative reciprocals, create the equation of the perpendicular to the chord that passes through the calculated mid-point.

Then do the same thing for and .

Now you have two linear equations in two variables that we know intersect at the circle's center. Solve the system of equations to determine the circle center, (h, k).

Once you determine the center point, use the distance formula to find the distance between the center and any one of your given points. That will be the circle radius, r.

Your equation will then be