Solving system equations with three unknowns

BasOomen

New member
Joined
May 19, 2019
Messages
4
I was reviewing an exam correction model and I stumbled upon a question about determining the equation of a circle. There were three points, all on the circle, which you could fill in into the standard equation for a circle, \(\displaystyle (x-a)^2 + (y-b)^2 = r^2\), in order to obtain a system of equations. They say you can solve this system but whenever I've tried this I've not come up with the right values: \(\displaystyle a = -1, \; b = -\tfrac{1}{2} \; \text{and} \; r = \sqrt{\tfrac{85}{4}}\). You can see the exact context in the image. Can someone help me solve this system of equations?

< broken attachment removed >
 

JeffM

Elite Member
Joined
Sep 14, 2012
Messages
3,422
I cant see the image. What are the points?
 

BasOomen

New member
Joined
May 19, 2019
Messages
4
I cant see the image. What are the points?
The image has the correction model which shows the points, filled into the general equation for a circle: \(\displaystyle B: \; a^2 + (4-b)^2 = r^ 2, C: \; (-4+a)^2 + (-4-b)^2 = r^2, P: \; (2-a)^2 + (3-b)^2 = r^2\)
 

BasOomen

New member
Joined
May 19, 2019
Messages
4
Maybe you can see the full image now (I've changed it to a JPEG-format).
 

Attachments

BasOomen

New member
Joined
May 19, 2019
Messages
4
There was a mistake in my writing which resulted in me using the right method but not getting the right answer. I noticed this after someone solved it for me.
 
Top