Answer:
r = 7
Explanation:
equation of circle is (x - a)² + (y - b)² = r²
where a is x-coordinate of centre of circle, b is y-coordinate of centre of circle, r is the radius. radius = half of diameter.
x² - 8x + y² - 10y = 8
we need to complete the sqaure for both x and y
x² - 8x = (x - 4)² = x² - 8x + 16, which is 16 more than x² - 8x. so we need to subtract that 16.
we now have (x - 4)² - 16.
now do the same with y
(y - 5)² = y² - 10y + 25, which is 25 more than y² - 10y. so we need to subtract 25.
we now have (y - 5)² - 25.
back to our full equation.
(x - 4)² -16 + (y - 5)² - 25 = 8
(x - 4)² + (y - 5)² - 41 = 8
(x - 4)² + (y + 5)² = 49 = r²
radius r = √49 = 7