A circle has equation x^2 + y^2 - 8x - 10y + 5 = 0, find its centre and radius
To find the centre and radius of the circle, you need to get the equation into the form (x - a)2+ (y - b)2= r2. You can do this by rearranging to bring the x and y parts together, and completing the square. Once that's done, you can find the centre at coordinates (a, b) and the radius is r.So, bringing the x and y components together, x2 + y2 - 8x - 10y + 5 = (x2 - 8x) +(y2 - 10y) + 5 = 0. Then completing the square for x gives you (x2 - 8x) = (x - 4)2 - 16 and completing the square for y gives you (y2 - 10y) = (y - 5)2- 25. Substituting these back into the original equation and rearranging, you get (x - 4)2 - 16 + (y - 5)2- 25 + 5 = (x - 4)2 + (y - 5)2 - 36 = 0. So (x - 4)2 + (y - 5)2 = 36.So, you can read off the centre of the equation as (4, 5) and the radius is the square root of 36, which is 6.
