# System of linear equations

IniquiTrance

## Homework Statement

Find coefficients a, b, c, d so that the circle with the following 3 points satisfies the equation:

$$ax^{2} + ay^{2} + bx + cy + d = 0$$

Points:

(-4, 5)
(4, -3)
(-2, 7)

## The Attempt at a Solution

I'm wondering if since I can only construct 3 equations from the 3 points, if I will have to make one unknown a parameter - probably d.

Is there a way to construct a 4 th equation which I'm missing?

Thanks!

Homework Helper
The parameters a,b,c and d are not independent if you are given that it's a circle. Write the equation of a circle in the form (x-a)^2+(y-b)^2=r^2. Now you only have three parameters. And you have three points.

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IniquiTrance
What if I used Gauss Jordan elimination to find a,b and c in terms of parameter d, would that sufficiently answer the question?