Solving Equations of Circles: Finding Center and Radius | Homework Help

[morrowcosom]

Homework Statement

Here is the equation of a circle:
x^2 + y^2 - 3x + 7y - 6 = 0


It is your job to find the center and the radius of the circle.

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Enter the coordinates of the center and the radius (as numbers):

Homework Equations

(x-a)^2+(y-b)^2=r^2
(a,b)=center

The Attempt at a Solution

The problem: x^2 + y^2 - 3x + 7y - 6 = 0
(x-3/2)^2+(y-(-7/2)^2

(x-3/2) (x-3/2)= x^2 -3/2x -3/2x +9/4= x^2-3x+9/4
(y+7/2) (y+7/2)= y^2 +7/2y +7/2y +49/4= y^2+7y+49/4

So, x^2+y^2-3x+7y-29/2= -sqrt(17/2)

I am doing independent study on a computer program. I have the values for the x and y coordinates right, but my value for the radius (sqrt(17/2)) is not right. I do not understand this because when I square this radius and move it over to the other side I get -6 just like the original equation of x^2 + y^2 - 3x + 7y - 6 = 0. What am I doing wrong?

 

[LCKurtz]

Try arranging your work like this:

x² - 3x + y² + 7y = 6

Now add to both sides:

x² - 3x + 9/4 + y² + 7y + 49/4= 6 + 9/4 + 49/4

(x - 3/2)² + (y + 7/2)² = 82/4 = 41/2

Now you can read off the center and radius.