How do you find the center and radius of the the circle x^2 + y^2 + 6/5x - 8/5y - 8 = 0x2+y2+65x−85y−8=0?

1 Answer
Rory H.
Feb 13, 2016

First factorise the original equation, so that you have it in the form of a circle equation:
(x+3/5)^2+(y-4/5)^2=9(x+35)2+(y−45)2=9
From this we can see that the radius =sqrt(9)=3=√9=3, the centre x-coordinate is -3/5=-0.6 and the centre y-coordinate is 4/5=0.8.

Explanation:

Starting with the original equation:
x^2 + y^2 + 6/5 x - 8/5 y - 8 = 0x2+y2+65x−85y−8=0
which equals:
x^2 + 6/5 x + y^2 - 8/5 y + (1 - 9)x2+65x+y2−85y+(1−9)

= x^2 + 6/5 x + 9 /25 +y^2 - 8/5 y +16/25 - 9x2+65x+925+y2−85y+1625−9

Now factorise the above equation, so that you have it in the form of a circle equation:
(x+3/5)^2+(y-4/5)^2=9(x+35)2+(y−45)2=9

The circle equation is:
(x-x_0)^2+(y-y_0)^2=r^2(x−x0)2+(y−y0)2=r2

Where r is the radius. The centre x point and the centre y point are x_0 and y_0x0andy0 respectively.

From this we can see that the radius =sqrt(9)=3=√9=3, the centre x-coordinate is -3/5=-0.6 and the centre y-coordinate is 4/5=0.8.

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