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.